Practice Exam 2 - Chapter 5
Name:
Instructions:
Give yourself 50 minutes to complete this practice exam.
Justify each answer.
Record your answer in the answer fields.
Each answer has equal weight.
1.
12.
2.
13.
3.
14.
4.
15.
5.
16.
6.
17.
7.
18.
8.
19.
9.
20.
10.
21.
11.
22.
For #1-#6, when tan (θ) = 92 and cos (θ) < 0, evaluate (if possible) all six
trigonometric functions of θ.
1. sin (θ) =
2. cos (θ) =
3. tan (θ) =
4. csc (θ) =
5. sec (θ) =
6. cot (θ) =
sec4 (x) − tan4 (x)
.
7. Factor and simplify
sec2 (x) − tan2 (x)
8. Add and simplify
cos(θ) sin(θ)
+
.
sin(θ) cos(θ)
For #9 - #12, verify the identity.
9. sin x sec x = tan x
10. sec2 x tan2 x + sec2 x = sec4 x
11.
csc x + sec x
= cot x + tan x
sin x + cos x
12. (sin x + cos x)2 = 1 + sin 2x
13. Rewrite sin
2
x
2
in terms of the first power of cosine.
14. Use a half-angle formula to simplify the expression
15. Rewrite 4 cos(3x) cos(2x) as a sum or difference.
16. Rewrite cos(x) − cos(3x) as a product.
sin(4x)
.
1 + cos(4x)
Find all solutions of the equation in the interval [0, 2π)
17. cos2 (x) + cos(x) = 0
18. cos(2x) − cos(x) = 0
19. 4 sin2 (x) + 3 = 0
20. tan(3x) = 0
21. Find the exact value of cos(15◦ ) using the fact that 15◦ = 45◦ − 30◦ .
22. Use the figure to find the exact value of sin(2θ), cos(2θ), tan(2θ).
(3, 2)
θ