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Pre-Calculus
5.1 – 5.2
Review Worksheet
Name ___________________________
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1. Find sin Ө and cos Ө of tan Ө = ¾ and sin Ө > 0.
Simplify
2. (sin x + cos x)2 + (sinx – cos x)2
4.
sin x cos x
1 − cos 2 x
5.
cosθ
1 + sin θ
+
1 + sin θ
cosθ
tan(
2
cot x
7.
+ sin x csc x
1 + csc x
Prove.
cos x
1 − sin x
10.
=
1 + sin x
cos x
3. csc A – cos A cotA
8.
6. cos3y + cosy sin2y
π
− x) csc x
2
csc 2 x
9. (sin x)(tanx + cot x)
11.
sin x cos x
+
= sin x csc x
csc x sec x
12.
sin θ
tan θ
=
sin θ + cosθ 1 + tan θ
13. cot2x – cos2x = cos2cot2x
14. Solve for 0 < x < 2π. Give answers to three decimal places if not the exact value.
a. 4 cos2x – 4 cosx + 1 = 0
c. cos2x – 2 cos x = -1
e. tan2x = 2tanxsinx
b. tan2x = 3
d. 2 cos2x = cosx
f. 2csc2x = 3 cot2x – 1