Precalculus
Sections 6.1-6.4 Quiz Review
Name: __________________
Period: ____
Use of the “Trig Cheat Sheet” will be allowed on the quiz.
Verify the equations are identities. Choose only one side and alter it to be identical
to the other side.
1. cot x(tan x  cot x)  csc2 x
2.
1  cos x
 csc x
sin x  cos x sin x
3.
cot x cos x cos x  1


sec x sin x
tan x
Verify the equations are identities. Choose only one side and alter it to be identical
to the other side.
4.
sin 
 csc   cot 
1  cos 
5.
1
 cot x csc x
sec x  cos x
6.
sin 4 x  cos 4 x
 2  csc2 x
2
sin x
45
with θ in QIV, state the value of the other five trig functions
27
using trig identities (other methods are not acceptable).
7. Using sec  
8. Find the exact value (e.g.
3
) of the expression given using a sum or difference
2
identity:
a. cos135 ,
b. sin105
c. tan
11
.
12
9. Use a half-angle identity to find exact values for sinθ, cosθ, and tanθ for the given
value of θ:
5
a.  
12
b.   112.5
10. Find the exact value of the given expression:
3

tan( )  tan( )
20
10
a.
3

1  tan( ) tan( )
20
10
b.
11. Given α and β are obtuse angles with tan   
difference identities find:
a. sin(a - b )
b. cos(a + b )
c. tan(a - b )
60
35
and sin  
, using sum and
11
37
12. Rewrite in terms of an expression containing only cosines to the power 1:
a. 4cos4 x
b. 3sin 4 x
13. Use a double-angle identity to find exact values for the following expression:

a. 2 cos 2 ( )  1
12
 
2 tan  
 12 
b.
 
1  tan 2  
 12 
c.
14. Find the exact value using product-to-sum identities:
 7
a. sin 
 12
   
 sin 

  12 
b. 2 cos15 sin135
15. Write the sum as a product using the sum-to-product identities:
a. cos  9h   cos  4h 
11x
5x
)  sin( )
b. sin(
8
8