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
©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
©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
©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
©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
©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
©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
©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
©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
©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
©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
©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
©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
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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