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Pre Calculus
Unit 9 Review 1
This test is cumulative over ALL trig taught so far!!!
Simplify the following trigonometric expressions.
1. sinx cos2x - sinx
2. sinA + cot A cos A 3.
Factor Completely. 5. tan2 x – 25
Simplify 7.
sin x
 cot x
1  cos x
4.
6. cot2(A) - cot(A) - 12
cos x 1  sin x

1  sin x
cos x
8.
sec2 x  1
sin 2 x
1
1
(
 cos x)
sin x cos x
Prove the 4 identities shown below. Remember to show all steps, completely and neatly. If your work can not be
read or followed, it would be counted wrong. (Separate Paper!)
Show work going down.
9.
11.
sec2 A  1
 sin 2 A
sec2 A
sin x
 csc x  cot x
1  cos x
10.
4
4

 8 csc 2 x
1  cos x 1  cos x
12.
tan x + cot x = sec x csc x
Solve the following problems using the appropriate sum and difference identities.
SHOW ALL WORK!
4
4
and Cos  
,
find cos (   ).
7
13
4
4
14. Given Sin  =
and  is in Quad II and Cos   
with  in Quad III.
Find sin (   ).
7
13
7
15. Find cos 255 
16. Find sin
12
13. Angles

and
 are both in the QI. Sin  =
Pre Calculus
Unit 9 Review 1
This test is cumulative over ALL trig taught so far!!!
Simplify the following trigonometric expressions.
1. sinx cos2x - sinx
2. sinA + cot A cos A 3.
Factor Completely. 5. tan2 x – 25
Simplify 7.
sin x
 cot x
1  cos x
4.
6. cot2(A) - cot(A) - 12
cos x 1  sin x

1  sin x
cos x
8.
sec2 x  1
sin 2 x
1
1
(
 cos x)
sin x cos x
Prove the 4 identities shown below. Remember to show all steps, completely and neatly. If your work can not be
read or followed, it would be counted wrong. (Separate Paper!)
Show work going down.
9.
11.
sec2 A  1
 sin 2 A
sec2 A
sin x
 csc x  cot x
1  cos x
10.
4
4

 8 csc 2 x
1  cos x 1  cos x
12.
tan x + cot x = sec x csc x
Solve the following problems using the appropriate sum and difference identities.
SHOW ALL WORK!
4
4
and Cos  
,
find cos (   ).
7
13
4
4
14. Given Sin  =
and  is in Quad II and Cos   
with  in Quad III.
Find sin (   ).
7
13
7
15. Find cos 255 
16. Find sin
12
13. Angles

and
 are both in the QI. Sin  =
Solve the following trig equations for the indicated domain.
17. 2sinA – 1 = 0 ; for all angles in degree measure
18. 2sin2u – sin u - 1 = 0 ; for [0, 360]
3
= 0; for all angles in radian measure.
3
20. 4 cos2  - 1 = 0 for 0    180
2
21. 2cos   3cos   1 for 0    360
1
Review: 22. Evaluate Arccos ( ) in degrees.
2
2
23. The period of the function f(x) = 4cos
(x+2) is:
3
7
24. Find the exact value for sin
.
4
19. tan A –
25. Find the asymptotes for the following two equations:
a.

b. y  3cot 3(  40)
y  5 tan 2( x  )
3
3
)
3
y  3cos 2(  45)
26. Find all the angles in radian measure for Arc tan( 
Graph two full cycles of the following graphs:
28. y  2 csc

6
( x  4)
29. y 
27.
1

cot 2( x  )
4
4
Solve the following trig equations for the indicated domain.
17. 2sinA – 1 = 0 ; for all angles in degree measure
18. 2sin2u – sin u - 1 = 0 ; for [0, 360]
3
= 0; for all angles in radian measure.
3
20. 4 cos2  - 1 = 0 for 0    180
2
21. 2cos   3cos   1 for 0    360
1
Review: 22. Evaluate Arccos ( ) in degrees.
2
2
23. The period of the function f(x) = 4cos
(x+2) is:
3
7
24. Find the exact value for sin
.
4
19. tan A –
25. Find the asymptotes for the following two equations:
b.

b. y  3cot 3(  40)
y  5 tan 2( x  )
3
3
)
3
y  3cos 2(  45)
26. Find all the angles in radian measure for Arc tan( 
Graph two full cycles of the following graphs:
28. y  2 csc

6
( x  4)
29. y 
27.
1

cot 2( x  )
4
4