Exam: 250312RR - Analytic Trigonometry
1. Rewrite the following expression as a simplified expression containing one term.
2. Use the figure below to find the exact value of the trigonometric function cos 2θ.
3. Express the product of sin 5x cos 2x as a sum or difference.
4. Use a half-angle formula to find the exact value of the expression sin 165°.
5. Using a double-angle formula, find cos 420°.
6. Complete the following identity:
A. sin x tan x
B. 1 + cot x
C. sec x csc x
D. - 2tan
7. Use the figure to find the exact value of the trigonometric function cos 2θ.
8. 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°
9. Complete the identity given below.
(sin x - cos x)
A. sin 2x
B. 1 - cos 2x
C. 1 - sin 2x
D. 1 + cos 2x
10. Which expression could you use to help you evaluate .
11. Use the given information to find the exact value of the expression sin 2θ.
12. Use a calculator to solve the following equation on the interval Round the answer to two
decimal places.
sin x = -0.29
A. 0.29, 5.99
B. 0.29, 3.44
C. 0.29, 1.87
D. 3.44, 5.99
13. Find all solutions of the equation
14. Write 2 sin x cos 6x as a sum or difference of trigonometric functions.
A. cos 5x + cos 7x
B. sin 7x - sin 5x
C. cos 5x - cos 7x
D. sin 7x + sin 5x
15. Find the exact value of the expression cos (245° - 5°).
16. Use trigonometric identities to find the exact value of the following expression.
17. Solve the following equation on the interval
18. To which of the expressions below is equivalent?
19. Use a half-angle formula to find the exact value of the expression cos 112.5°.
20. Find the exact value of the following by using a sum or difference identity.
sin (185° - 65°)
