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Chapter 4 Problem Packet
4.1 Angle Measure
Find the radian measure of the angle with the given degree measure.
1. 40
2. 330
3. 30
4. 45
5. 150
6. 765
Find the degree measure of the angle with the given radian measure.
7.
10.
7
2
3
4
8.
5
6
9. 

5
11.

18
12. 2.5
The measure of an angle in standard position is given. Find two positive angles
and two negative angles that are coterminal with the given angle.
13. 300
15.
11
6
14. 135
16. 

4
The measures of two angles in standard position are given. Determine whether
the angles are coterminal.
17. 70 , 430
18. 55 ,325
1
19.
5 17
,
6 6
20.
32 11
,
3
3
Find an angle between 0o and 360o that is coterminal with the given angle.
21. 733o
22. 361o
23. -100o
Find an angle between 0 and 2  that is coterminal with the given angle.
7
3
24.
12
5
25. 
27.
51
2
28. 10
26.
13
4
Find the missing arc, angle, or radius measure.
29.
30.
31.
32. How many revolutions will a car wheel of diameter 30 in. make as the car
travels a distance of one mile?
35. Find the distance that the earth travels in one day in its path around the
sun. Assume that a year has 365 days and that the path of the earth around
the sun is a circle (it’s actually an ellipse) of radius 93 million miles.
2
Trigonometry of Right Triangles
Find the values of the six trigonometric ratios of the angle  in the given
triangles
1.
2.
3.
Find (a) sin  and cos  , (b) tan  and cot  , and (c) sec  and csc  .
4.
5.
Find the side labeled x. State your answer as an exact value.
6.
7.
3
8.
9.
11.
Sketch a triangle that has an acute angle  , and find the other 5
trigonometric ratios of  .
12. sin  
14.
3
5
13.
tan   3
cos  
2
7
15. sec  7
Evaluate the expression.
16. sin

6
 cos

17. sin 30 csc 30
6
18. sin 30 cos 60  sin 60 cos 30
19. (sin 60 )2  (cos 60 )2
4
20. (cos30 )2  (sin 30 ) 2
Solve the right triangle.
21.
22.
23.
24. The angle of elevation to the top of the Empire State Building in New
York is found to be 11o from the ground at a distance of 1 mi. from the base
of the building. How tall is the Empire State Building?
25. A 96-ft. tree casts a shadow that is 120-ft. long. What is the angle of
elevation of the sun?
26. A water tower is located 325 ft from a building. From a window in the
building it is observed that the angle of elevation to the top of the tower is
39o and the angle of depression to the bottom of the tower is 25o. How tall is
the tower? How high is the window?
5
Find x correct to one decimal place.
27.
28.
29.
4.3 Trigonometric Functions of Angles
Find the reference angle for the given angle.
1. 225o
2. -35o
3. 181o
4. 290o
5. 750o
6. 570o
7. -95o
8. 165o
9.
3
5
13. 

4
10.
7
6
11. 
14.
23
11
15.
6
2
3
23
11
12.
17
3
16.
3
2
Find the exact value of the trigonometric function by applying reference
angles.
17. sin1500
18. cos 2250
21. sec(60)0
22. sin
2
3
23. cos
7
6
24. tan
5
6
 

 4
26. sin
11
3
27. csc
7
3
28. tan
5
2
7
4
30. sin  
25. cot  
29. cos
19. sin1350
20. tan 3300
 5 

 6 
Find the quadrant in which  lies from the information given.
31. sin   0 and cos  0
32. tan   0 and sin   0
33. sec  0 and tan   0
Find the values of the trigonometric functions of  from the information given.
34. sin  
3
,  in quadrant II
5
36. tan  
3
, cos  0
4
35. cos   
7
7
,  in quadrant III
12