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Review for Exam
1. (sec x - csc x) sin x cos x =
A. sin x - cos x
B. cos x - sin x
C. sin x + cos x
D. cos x + sin x
E. none of these
2. Let be an acute angle in standard position. Find the quadrant containing the terminal side of , if csc  < 0
and sec  < 0.
A. I
B. II
C. III
100
3. Determine which quadrant
lies.
11
D. IV
E. V
A. I
B. II
C. III
D. IV
E. V
C. -0.788
D. -0.692
E. -0.573
4. Compute sin 256°
A. -0.999
B. -0.970
In problems 5 and 6 , consider a right triangle ABC as shown below
B
c
5. Determine B if c = 11.5 and b = 6.8
A. 32  58’
a
B. 34  4’
C. 35  22’
D. 36  15’
6. Determine a if B = 43 and b = 3.5
A
b
C
A. 1.76
7. Determine if sin  = 0.675, if
A. 2.40
B. 2.33
B. 3.01

2
C. 3.26
D. 3.75
 
C. 1.89
D. 1.38
E. 0.74
5
2
E. 3
8. What is the period of y  3 sin( 5 x) ?
A. 2
B.
2
5
C. 5
9. Let be an acute angle such that sin  
A.
24
7
B.
7
24
C.
D.
24
. Find the value of tan
25
7
25
D.
25
7
E.
25
24
10. Convert 3 radians to degrees.
A. 0.052 
B. 343.8 
C. 180 
D. 171.9 
E. None of these
3
12
in quad II and cos   
in quad II, find cos(   )
5
13
33
99
33
63
63
A. 
B.
C.
D. 
E.
65
65
65
65
65
11. Given sin  
12. Which of the following is the equation of the graph to the left?
13. Determine the exact value of sin
A.
1
2
B.
A. y  2 sin 2 x
B. y  2 cos 2 x
C. y  2 cos 2 x  1
D. y  sin 2 x  1

3
2
2
C.
3
2
D.
2
E.
1
14. Find the amplitude of y  5 cos( 4 x)  3
A. 3
15.
B. 4
D.

2
E.

4
sec2   1
=
sec2 
A. sin 2 
16.
C. 5
B. cos2 
C. tan 2 
D. cot 2 
B. 2 cos2 x
C. 2 sec2 x
D. 2 csc2 x
1
1


sin x  1 sin x  1
A. 2 sin 2 x
17. Given cos  
A. 
14
9
7
in quad III, find sin2
9
56 2
32
B. 
C. 
81
81
D.
49
18
E. None of these
18. Evaluate: sin105
A.
6 2
4
19. cos

6
cos
A. cos

4
 sin
B.
6 2
4


6
sin
5
12
4
2 6
4
C.
D.
1 3
2
E. None of these
=
B. sin
5
12
  
D. sin   
 12 
  
C. cos  
 12 
E. None of these
20. Which of the following is the equation of the graph to the left?
 x
A. tan  
2
B. tan x
C. tan 2x
x
D. cot  
2
21. Solve the following trigonometric equation for 0  x  2 :
2 sin 2 x  3 sin x  1  0
A.
  5
,
6 2
,
6
B.
  5
,
3 2
,
3
C.

6
, ,
7
6
22. Find the following values in exact form: Cos1 ( 
23. Consider a given angle B whose location is
D.
18
3
,
E.
  7
, ,
6 2 6
3
5
B
 B  2 with a secant value of sec B = . Find cos in
2
3
2
24. Find the area of the oblique triangle (to 3 decimal places):
B
6
100º
50º
3
,
3
) _________
2
exact form.
A
 2
C
Solve each triangle. Round answers at the end.
25. A = _______
B
B = _______
b = _______
7
C
B
26. A = _______
a = ________
b = ________
10
5
40º
A
A
3

 cos
2
2
27. Simplify:
sin   cos 4
sin
a)
1  2 
sec

2  3 
b) tan
5
4
c) 2 cos
7
6
d)  cos 
e) cos
28. In what quadrant does the terminal side of an angle with the measure of
a) I
b) II
c) III
6
5
3
2
lie?
d) IV
29. Which of the following are a coterminal and the reference angle for   73 ?
a) 107° and 73°
b) 17° and 107°
c) -253° and 73°
d) 287° and 73°
30. What is 240° in radian measure?
a)
3
2
b)
3
4
c)
31. What is the approximate degree measure of
a) 96.92°
b) 304.5°
7
13
4
3
d)
43200

?
c) 96.55°
d) 1.41°
32. Using the triangle below, find sec .
9
θ
5
a)
9 14
28
b)
106
5
c)
9
5
d)
106
9
140º
20º
C
33. If sin  
1
and tan   0 , what is cos θ?
5
a) 
26
5
b)
2 6
5
c) 
2 6
5
26
5
d)
34. If the point (5, -12) is on the terminal side of θ, what is sin θ?
a.) 135
b)  125
c)  12
13
d)  125
35. What is the amplitude and period of the graph of y  3sin 4x    ?
a) 4 and 3
b) 3 and 4
c) 4 and 
d) 3 and

2
36. If the angle the sun makes with the ground is 25°, what is the approximate length of a shadow cast by a
person that is 6 feet tall?
a) 12.87 ft.
b) 14.20 ft.
c) 2.80 ft.
d) none of these
37. Which of the following is the graph of y  4 cos 12 x ?
38. What is the radian value of cos 1  21  ?
a.

6
b)  3
c)
2
3
d)

3
39. Using factoring and the trigonometric identities, to what would cos 2 x  sin 2 x cos 2 x simplify?
b. 1 sin 2 x
40. If cos  
c.
b) 2 cos x
c) cos 4 x
d)  cos 4 x
3
and  is in quadrant II, what is the exact value of sin 2 ?
5
24
25
b)
4
5
c)  24
25
d)
16
5
41. For the interval [0,2 ) , what are the solutions to the equation 2 cos x  3  0 ?
a)
2
3
, 43
b)
5
6
, 76
c)

6
, 116
d)

3
, 53
42. Given A = 41°, B = 72° and a = 15, what is the approximate length of c?
a) 19.6
b) 7.8
c) 10.7
d) 21.0
43. Given a = 2178, b = 23°, and c = 1719, what is the approximate length of b?
a) 2184.9
b) 2062.1
c) 805937.8
d) 897.7
For questions # 44 – 47, decide how many possible triangles there given the following information.
a) 0 triangles
44. A = 54°, b = 19, C = 61°
45. a = 3, b = 5, c = 6
46. A = 105°, b = 4, C = 130°
47. A = 30°, a = 16, c = 14
b) 1 triangle
c) 2 triangles