Chapter 10 - NCPN

Practice and Problem Solving
Use a double-angle or half-angle identity to find the exact value
of each expression.
5. cos 120° − 1 2
6. sin 90° 1
7. cos 90° 0 8. sin 240° − 3
2
9. tan 240° 3 10. sin 15° 2−
3
11. tan 15° 7− 4 3 12. sin 120°
13. tan 300° − 3 14. cos 15°
15. tan 120° − 3 16. sin 60°
2
3
2
2+
3
2
3
2
17. cos 60° 1 2 18. cos 150° − 3
2
19. tan 60° 3 20. sin 22.5°
2−
2
2
21. cos 600° − 1 2 22. tan 22.5° 3−
2 2
23. cos 240° − 1 2
24. cos 22.5°
2+
2
2
25. Find cos 2θ if cos θ = − 2 5 and 90° < θ < 180°. − 17
25
26. Find cos θ if sin θ = − 24
25 and 180° < θ < 270°. − 7
27. Find tan
2 θ if cos θ = 4 5 and 270° < θ < 360°. 1 3
25
28. Find sin θ 2 if cos θ = 1 2 and 0° < θ < 90°. 1 2
29. The sound waves generated by a vibrating tuning fork
can be modeled by the function y = 2sin θ. If the
tuning fork vibrates twice as fast, the sound
will be one octave higher. This is given by
the function y = 2sin 2θ. Write the
function in terms of θ to model the
higher octave sound waves. y = 4 sin θ cos θ
30. How could the identity for cos A 2 be
derived from the identity for cos 2A
Show your work. see margin
10.8 Double-Angle and Half-Angle Identities 483