Name__________________________________Date_________Class_____
Sections 4.1-4.4 Review
Pre-AP Precalculus
Graphing calculators are allowed on this portion only.
Use a protractor to sketch each angle in standard position and state the
quadrant (or axis) in which it is contained. Label the angle and the
reference. Indicate the direction of the angle.
1. -115
4.
5
3
2. 225
5. 
3. 400

6.
10
Determine one positive and one negative co-terminal angle.
7. 900
9.
11
4
8. 145
10.

2
8
5
Find, if possible, the complement and supplement of each angle.
11. 20
13.
12. 31
5
8
14.
2
5
Find the exact radian measure of the angle given in degrees.
15. 300
16. 10
17. 150
Find the degree measure of the angle given in radians.
18.
16
9
19.
3
4
20.
7
3
21. Find the length of the arc on a circle with a central angle of 120 and a radius of
6 ft.
22. Find the measure of the central angle (in degrees) that intercepts an arc
inches long in a circle of radius 12 inches.
23. Find the length of the arc intercepted by a central angle of
radius 12 centimeters.
38
5

radians in a circle of
4
24. Find the radius of a circle in which a central angle of 60 intercepts an arc 15
inches long.
25. Find the measure of the central angle (in radians) in a circle of radius 18 inches
that intercepts an arc 15 inches long.
26. Find the radius of a circle in which a central angle of
40
millimeters long.
9
10
radians intercepts an arc
9
Find the values of the five remaining trigonometric functions with the given
constraints.
27. sin  
4
, cos   0
5
29. tan  3 , sin  0
31. cos   
8
, csc   0
17
28. sec   2, tan  0
30. csc    5 , cot   0
32. cot   
1
, sec   0
2
This portion is to be completed without the aid of a graphing calculator.
Find the exact value of each expression or state that the value is undefined.
33. sin 390
34. cos 135
35. tan 300
36. sec 495
37. csc (-210)
38. cot 180
39. csc (-630)
40. tan 315
41. sin 120
 
44. cos   
 6
42. tan
5
4
 7 
43. sin  

 3 
45. csc
5
2
46. sec
9
4
47. cot 3
48. sin
2
3
49. tan
7
6
50. cos
4
3
Find θ for 0 ≤ θ < 2.
51. cot   1
52. sin  1
53. tan   3
54. cos  
55. sec    2
56. csc   
57. cos   0
58. sec   1
1
2
2 3
3
Find θ using the given restraints.
59. sin   
61. tan  
2
2
3
3
2    2
60. cot   0
3
  0
2
62. csc   2



3
63. Find all values of θ, -2Ä ≤ θ ≤ 2Ä, for which tan  is undefined.
64. Find all values of θ, 0 ≤ θ ≤ Ä, for which csc  is undefined.
5

 
2
2
   4