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1. Use trigonometric identities to find the exact value of the following expression.
2. Using a double-angle formula, find cos 420°.
3. Use a half-angle formula to find the exact value of the expression sin 165°.
4. Find the exact value of the expression below.
5. Find all solutions to .
A. for any integer n
B. for any integer n
C. for any integer n
D. for any integer n
6. Identify α and β in the following expression, which is the right-hand side of the formula for cos (α – β).
cos (170°) cos (50°) + sin (170°) sin (50°)
A. α = 50°, β = − 170°
B. α = − 50°, β = 170°
C. α = − 170°, β = 50°
D. α = 170, β = 50°
7. Solve the problem sin 8x – sin 2x.
A. 2 sin 5x cos 3x
B. 2 sin 3x
C. 2 cos 2x cos 5x
D. 2 sin 3x cos 5x
8. Complete the identity given below.
(sin x − cos x)2 = ?
A. 1 + cos 2x
B. 1 − cos 2x
C. sin 2x
D. 1 − sin 2x
9. Find the exact value of the expression cos (245° − 5°).
10. Rewrite the following expression as a simplified expression containing one term.
11. Use a calculator to solve the following equation on the interval Round the answer to two decimal places.
sin x = −0.29
A. 3.44, 5.99
B. 0.29, 5.99
C. 0.29, 1.87
D. 0.29, 3.44
12. Find the exact value of the expression .
13. Express the product of sin 5x cos 2x as a sum or difference.
14. Complete the following identity:
A. 1 + cot x
B. − 2tan2 x
C. sin x tan x
D. sec x csc x
15. Find all solutions of the equation
16. Find the exact value of the following by using a sum or difference identity.
sin (185° − 65°)
17. use the figure below to find the exact value of the trigonometric function cos 2θ.
18. Solve the following equation on the interval
19. Which expression could be used to fill in the blank in sin x _______ = tan x to create a valid trigonometric identity?
A. sin x
B. tan x
C. cos x
D. sec x
20. Use the given information to find the exact value of the expression sin 2θ.
