Analytic Trigonometry
1. Use a half-angle formula to find the exact value of the expression sin 165°.
2. Identify a and ß in the following expression, which is the right-hand side of the formula for cos (a – ß).
cos (170°) cos (50°) + sin (170°) sin (50°)
A. a = – 170°, ß = 50°
B. a = 50°, ß = – 170°
C. a = – 50°, ß = 170°
D. a = 170, ß = 50°
3. Find all solutions to .
A. for any integer n
B. for any integer n
C. for any integer n
D. for any integer n
4. Use the figure below to find the exact value of the trigonometric function cos 2?.
5. Which expression could you use to help you evaluate .
6. Solve the problem sin 8x – sin 2x.
A. 2 sin 3x cos 5x
B. 2 sin 3x
C. 2 cos 2x cos 5x
D. 2 sin 5x cos 3x
7. Write 2 sin x cos 6x as a sum or difference of trigonometric functions.
A. sin 7x – sin 5x
B. cos 5x + cos 7x
C. cos 5x – cos 7x
D. sin 7x + sin 5x
8. Solve the following equation on the interval
9. Using a double-angle formula, find cos 420°.
10. Complete the following identity:
A. sin x tan x
B. sec x csc x
C. 1 + cot x
D. – 2tan
2
x
11. Use a half-angle formula to find the exact value of the expression cos 112.5°.
12. Which expression could be used to fill in the blank in sin x _______ = tan x to create a valid
trigonometric identity?
A. sec x
B. tan x
C. sin x
D. cos x
13. Use trigonometric identities to find the exact value of the expression below.
14. Use the figure to find the exact value of the trigonometric function cos 2?.
15. Use trigonometric identities to find the exact value of the following expression.
16. To which of the expressions below is equivalent?
17. Rewrite the following expression as a simplified expression containing one term.
18. Express the product of sin 5x cos 2x as a sum or difference.
19. Find the exact value of the following by using a sum or difference identity.
sin (185° – 65°)
20. Find all solutions of the equation
