Transcribed Text
Review Exercises
4.1
1. Find the radian measure of the central angle of a circle of radius 6 centimeters that intercepts an arc of length 27 centimeters.
In Exercises 24, convert each angle in degrees to radians. Express your answer as a multiple of TT.
2) 15°
3. 120°
4. 315
In Exercises 57, convert each angle in radians to degrees.
5m 3
7z
6.
5
7.
5r
6
In Exercises 812, draw each angle in standard position.
6
9.23
10. 87
3
11.190°
12.135° 
In Exercises 1317, find a positive angle less than 360' or 27r that is coterminal with the given angle.
13. 400°
14. 445°
15.
13%
4
16.
31x
6
17.
8m
3
18. Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle. Express arc length in terms of TT. Then round your answer to two
decimal places.
19 The angular speed of a propeller on a wind generator is 10.3 revolutions per minute. Express this angular speed in radians per minute.
20. The propeller of an airplane has a radius of 3 feet. The propeller is rotating at 2250 revolutions per minute. Find the linear speed, in feet per minute, of the tip of
the propeller.
4.2
In Exercises 2122, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.
In Exercises 2122, a point P(x, y) is shown on the unit circle corresponding to a real numbert. Find the values of the
trigonometric functions at t.
y
I
21)
x
(1.0)
P=1111
22.
xd
(1.0)
p=1213
In Exercises 2326, use the figure shown to find the value of each trigonometric function at the indicated real number
or state that the expression is undefined.
y
3
1
V3
2
2
2
(0.1)
V3 1
2 2
116
V3 2 . 1/2 2
xd
(1,0)
(1.0)
V3 . 1
V3
1
2 2
2
2
(0.1)
1

2'
V3
2
1143
5%
23. sec
6
24. tan
4x
3
25. sec
II
2
26.cot TO
27
If
sin
t = use identities to find the remaining trigonometric functions.
257
In Exercises 2830 evaluate each expression without using a calculator.
28. tan 4.7 cot 4.7
29)sin² Il + cos² il
30. tan2 1.4  sec2 1.4
Chapter 4 Trigonometric Functions > Review Exercises
4.3
31. Use the triangle to find each of the six trigonometric functions of 0.
B
5
A
8
C
In Exercises 3235, find the exact value of each expression. Do not use a calculator.
32.
33.
34. 25tan"=
35. cos 2= sec"=
In Exercises 3637, find a cofunction with the same value as the given expression.
36. sin 70 .
37 cos *
2
In Exercises 3840, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.
B
38.
a
23°
A
100 mm
C
B
39,
c
20 cm
61° o
A
C
B
50 in.
40.
a
48°
C
A
41. Ifsin 9 = 1/4 and 0 is acute, find tan (=0).
42. A hiker climbs for a half mile up a slope whose inclination is 17° How many feet of altitude, to the nearest foot, does the hiker gain?
43. To find the distance across a lake, a surveyor took the measurements in the figure shown. What is the distance across the lake? Round to the nearest meter.
is
as
to
és
<
s
32°
it
50 m
44.
When a sixfoot pole casts a fourfoot shadow, what is the angle of elevation of the sun? Round to the nearest whole degree.
4.4
In Exercises 4546, a point on the terminal side of angle 0 is given. Find the exact value of each of the six trigonometric functions of 0, or state that the function is
undefined.
45. (1,5)
46. (0,1)
In Exercises 4748, let 8 be an angle in standard position. Name the quadrant in which 0 lies.
47. itan 0 > 0 and sec 0 > 0
48. tan 0 > 0 and cos 0 < 0
In Exercises 4951, find the exact value of each of the remaining trigonometric functions of 0.
49. cos 0 = 1/15 sin 0 < 0
50, tan 0 = 
51. cot 0
In Exercises 5256, find the reference angle for each angle.
52. 265'
53. 5%
8
54.  410
55. 17x
6
56.
11%
3
In Exercises 5767, find the exact value of each expression. Do not use a calculator.
57. sin 240*
58. tan 120'
7=
59. sec
4
60. COS 11x
6
61. cot ( 210°) 
62. CSC
=)
63. sin (
)
64. sin 495'
65. tan 13* 4
66. sin 22.T 3
67.cos
( 355)
4.5
in Exercises 6873, determine the amplitude and period of each function. Then graph one period of the function.
68. y = 3 sin 4x
69.y=2 cos 2x
70. y = 2 cos x
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