Download WS Review for TEST Chapter 5 Complete the expression using a

WS Review for TEST Chapter 5
Complete the expression using a fundamental identity.


1. sin   u  =
2. sin (-x) =
3. cot u =
2

1


5. tan   x  =
6.
=
7. sin 2 x + cos 2 x =
tan
x
2


9. Write 2 equivalent forms of the following identity:
4. sec 2  =
8. cot 2 x + 1 =
sec 2 u = 1 + tan 2 u
10. Use the given values to evaluate the remaining 4 trigonometric functions.
csc x =
 13
2
, tan x =
2
3
11. Factor the expression and use the fundamental identities to simplify.
cos 2 x sec 2 x – cos 2 x
12. Use the fundamental identities to write the expression in terms of a single trigonometric expression.
sec x
 sec x cos x
cos x
Identify the expression that completes the equation so that it is an identity. (Simplify)
cos 2 x
1  sin u
cos u
2
2
13. sin x (1 – csc x) =
14.
=
15.
=

cos u
1  sin u
1  sin x
Verify the identity.
sec x  csc x
16.
= csc x
1  tan x
6 tan x + 5 3 = 11 tan x
 4
2 5
A) x = ,
B) x =
,
3
3
3 3
17.
sin x
= sec x tan x
1  sin 2 x
18. Solve:
C) x =
4 5
,
3
3
D) x =
 5
,
3 3
Identify the x-values that are solutions of the equation.
20. 9 cot 2 x – 9 = 0
19. 10 cos x + 5 3 = 0
21. Find the exact value of cos (15). (Show your work.)
22. Find the exact value of sine, cosine, and tangent of the angle:
23. Find the exact value of the expression: sin
13
12

2

2
cos
+ cos sin
3
3
6
6
24. Find all solutions of the equation in the interval [0, 2).
2
2 



cos  x 
 + sin  x   =
2
3 
6


25. Verify the identity:
3 

cos  x 
 = sin x
2 

26. Find the exact values of sin 2 and cos 2 using the double angle formula.
5

sin  = , 0   
8
2
27. Find the exact value of tan

using the half angle formula:
2
cos  =
 56 
,
≤≤
65 2