Chapter 5 Problem Set
Name___________________________________
Complete the problems to the best of your ability. You may use your notes, textbook and calculator, but no additional
assistance. This is an individual assignment.
Verify the identities.
1.
sec 𝑥+tan 𝑥
√sec 𝑥−tan 𝑥
=
1+sin 𝑥
cos 𝑥
𝑐𝑠𝑐 2 𝑥−1
−
𝑐𝑜𝑠2 𝑥
2. 𝑠𝑖𝑛2 𝑥 (
𝑐𝑜𝑡 2 𝑥) = 𝑠𝑖𝑛2 𝑥
3. (sin 𝑥 − cos 𝑥)2 + 2 sin 𝑥 − cos 𝑥 = (1 + 2 sin 𝑥) (1 − cos 𝑥)
Solve the equation on the interval 0 ≤ 𝑥 ≤ 2𝜋
4. √3 tan 𝑥 sec 𝑥 + 2 tan 𝑥 = 0
5. cot 𝑥 − √3 = csc 𝑥
Express in terms of the sine, cosine, or tangent of one angle.
6. sin 50 cos 20  cos50 sin 20 
cos
7.

4
cos

3
 sin

4
sin

3

Use a sum or difference identity to find the exact value.
cos
8. sin 105°
Given:
9.
4

cos u  , 0  u 
5
2
sin v  

12

5
3
,  v
13
2
Draw a figure for u and v and find:
10.
cos  u  v 
Find all solutions of the equation in the interval [0, 2 ) .
12.

 1


sin  x    sin  x   
6
6 2


11.
tan  u  v 
Find the exact solutions of the equation in the interval [0, 2 ) .
13. 2cos x  sin 2 x  0
14. 4sin x cos x   3
Use a double angle formula to rewrite the expression.
15. 10sin x cos x 
sec u 
Given
sin
17.
u

2
2
16. 7  14sin x 
3
3
and
 u  2
5
2
. Draw a figure and find:
tan
18.
u

2