Double Angle And Half Angle Identities 2r2f16
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Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l
15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
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Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
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15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
Double-Angle and Half-Angle Identities ©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Use a double-angle or half-angle identity to find the exact value of each expression. 1) cos
7π 8
2) sin
3) sin 165°
1 4) sin 112 ° 2
5) sin 15°
6) cos
1 7) sin 22 ° 2
9) cos
23π 12
8) sin −
5π 12
10) sin 75°
3π 8
8 and 180° < θ < 270° 17
11) sin θ = −
θ
Find cos
7 3π and < θ < 2π 25 2 Find sin 2θ
12) sin θ = −
2
9 and 270° < θ < 360° 22 Find cos 2θ
13) sin θ = −
15) cos θ = − Find sin
7π 8
4 and −270° < θ < −180° 5
θ
14) cos θ =
4 and 270° < θ < 360° 5
Find cos
θ 2
4 π and 0 < θ < 5 2 Find cos 2θ
16) cos θ =
2
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t
Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities 1) − 5)
2+ 2 2 6− 2 4
2− 2 161 13) 242 9)
2
2) 6)
2− 2 6+ 4
2
3)
2
10)
6+ 4
14) −
3 10 10
6− 4
2
2− 2 2 17 11) − 17 7)
2
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l
15) −
3 10 10
2+ 2 2 − 6− 2 8) 4 336 12) − 625 4)
16)
7 25
Worksheet by Kuta Software LLC
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