Precalculus - Unit 5 Exam – 60 Points
Name _________________________________
Verify the following identities. (5 points each)
1)
cot x
= cos x
csc x
2) sin x cot x sec x = 1
!
!
3) sin 2 x cot 4 x tan 2 x = 1" sin 2 x
!
4) (sec x + tan x )(sec x " tan x ) = 1
!
5) csc x " cot x cos x = sin x
!
cos x + tan x
= cot x + sec x
sin x
8)
sin x
sin x
"
= 2cot x
1" cos x 1+ cos x
!
7)
!
6)
2 " 5cot x 2sin x " 5cos x
=
2 + 5cot x 2sin x + 5cos x
!
9) Find the exact value of (5 points)
a. sin 345°
!
b. cos345°
c) tan 345°
!
!
3
12
10) Given cos A = " , A in quadrant III and sin B = , B in quadrant II, find
5
13
a. sin ( A " B)
b. cos( A " B)
c. tan( A " B)
d. quadrant of ( A " B)
6
11) Given sin A = , A in quadrant II find
7
a. sin 2 A
b. cos2 A
d. quadrant of 2A
12) Given sin A =
(6 pts)
(6 pts)
"15
A
, A in quadrant III find cos
17
2
c. tan 2 A
(3 pts)