Name
Class
14-7
Date
Practice
Form G
Double-Angle and Half-Angle Identities
Use an angle sum identity to derive each double-angle identity.
1. cos 2 = cos   sin 2 
2. cos 2 = 2 cos   1
3. cos 2 = 1  2 sin 
4. sin 2 = 2 sin  cos 
2
2
2
Use a double-angle identity to find the exact value of each expression.
5. sin 120
8. cos 660
11. tan 660
6. tan 600
7. sin 660
9. tan 90
10. cos 90
12. sin 240
13. tan 120
Use a half-angle identity to find the exact value of each expression.
14. cos 15
15. cos 7.5
16. tan 7.5
17. sin 7.5
18. cos 45
19. tan 22.5
20. cos 22.5
21. sin 90
22. cos 90
Given sin =
23. cos

2
26. sec

2
7
and 90<  < 180, find the exact value of each expression.
25
24. sin
27. csc

2

2
25. tan

2
28. cot

2
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Name
Class
Date
Practice (continued)
14-7 Double-Angle and Half-Angle Identities
Given cos   –
8
and 180 <  < 270, find the exact value of each expression.
17
29. sin

2
30. cos

2
31. cot

2
32. tan

2
33. csc

2
34. sec

2
Verify each identity.
1  cos 2
35. cos 2  
2
36. cot  
37. tan  + cot  = 2 csc 2
38.
39. What is the exact value of cos 2 if sin  
 6
6
sin 2
1  cos 2
cos 2
 cot   tan 
sin  cos
 5
and 180 <  < 270?
3
 30
6
4 5
9
1
9
40. A scanner takes thermal images from altitudes of 300 to 12,000 m. The width
W of the swath covered by the image is given by W = 2H tan , where H is
the height and  is half the scanner’s field of view. Verify that
2 H  sin 2
 2 H  tan  .
1  cos 2
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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
64