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Chapter 4: Trigonometric Functions
1. Estimate the angle to the nearest one-half radian.
A)
B)
C)
D)
E)
Ans: B
Learning Objective: Estimate radian measure of angle
Section: 4.1
2. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)
8π
9
A) II B) III C) IV D) I E) The angle lies on a coordinate axis.
Ans: A
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
3. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)
–5π
8
A) III B) IV C) I D) II E) The angle lies on a coordinate axis.
Ans: A
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
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Chapter 4: Trigonometric Functions
4. Determine the quadrant in which the angle –6, given in radians, lies.
A) 1 B) 3 C) 4 D) 2
Ans: A
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
5. Determine the quadrant in which the angle 8, given in radians, lies.
A) 1 B) 3 C) 4 D) 2
Ans: D
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
6. Determine the quadrant in which an angle, θ , lies if θ = 5.50 radians.
A) 1st quadrant B) 2nd quadrant C) 3rd quadrant D) 4th quadrant
Ans: D
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
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Page 137
Chapter 4: Trigonometric Functions
7. Sketch the angle in standard position.
A)
B)
C)
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Chapter 4: Trigonometric Functions
D)
E) None of these
Ans: A
Learning Objective: Sketch angle in standard position
Section: 4.1
π
8.
Determine a pair of coterminal angles (in radian measure) to the angle 3
D)
A)
4π
2π
7π
5π
, –
, –
3
3
3
3
B)
E)
7π 4π
7π
2π
,
, –
3
3
3
3
C)
10π
2π
, –
3
3
Ans: D
Learning Objective: Identify angles coterminal to a given angle
Section: 4.1
.
9. Determine two angles (one positive and one negative, in radian measure) coterminal to
π
.
the angle 8
A)
D)
9π
15π
25π
23π
, −
, −
8
8
8
8
B)
E)
33π
23π
33π
15π
, −
, −
8
8
8
8
C)
9π
39π
, −
8
8
Ans: E
Learning Objective: Identify angles coterminal to a given angle
Section: 4.1
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Chapter 4: Trigonometric Functions
10. Determine a positive angle and a negative angle (in radian measure) coterminal to the
π
− .
angle 2
3π
5π
π
3π
π
3π
3π
π
π
5π
, −
, −
, −
, −
, −
2 E) 2
2
2
2
2
A) 2
B) 2
C) 1
D) 2
Ans: A
Learning Objective: Identify angles coterminal to a given angle
Section: 4.1
11.
Determine two coterminal angles (one positive and one negative) for
D)
A)
9π
11π
11π
3π
,−
,−
5
5
5
5
B)
E)
16π
14π
8π
2π
,−
,−
5
5
5
5
C)
14π
6π
,−
5
5
Ans: C
Learning Objective: Determine two coterminal angles (radians)
Section: 4.1
12.
θ=
4π
5 .
π
Find (if possible) the complement of 14 .
13π
11π
13π
3π
A) 28
B) 28 C) 14
D) 7
E) not possible
Ans: D
Learning Objective: Identify the complement of an angle
Section: 4.1
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Chapter 4: Trigonometric Functions
13. Find (if possible) the complement and supplement of the given angle.
A)
B)
C)
D)
E)
Ans: C
Learning Objective: Identify complement and supplement of angle
Section: 4.1
14.
11π
Find (if possible) the supplement of 13 .
2π
5π
12π
11π
A) 13 B) 13 C) 13
D) 26 E) not possible
Ans: A
Learning Objective: Identify the supplement of an angle
Section: 4.1
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Page 141
Chapter 4: Trigonometric Functions
15. Estimate, to the tens place, the number of degrees in the angle.
A)
B)
C)
D)
E)
Ans: E
Learning Objective: Estimate degree measure of angle
Section: 4.1
16. Determine the quadrant in which the angle lies.
–245°
A) Quadrant III B) Quadrant II C) Quadrant IV D) Quadrant I
Ans: B
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
17. Determine the quadrant in which the angle 41D lies.
A) 2 B) 3 C) 1 D) 4
Ans: C
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
18. Determine the quadrant in which the angle 12.3° lies.
A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV
Ans: B
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
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Chapter 4: Trigonometric Functions
19. Determine the quadrant in which the angle –220°35' lies.
A) Quadrant III B) Quadrant II C) Quadrant IV D) Quadrant I
Ans: B
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
20. Determine the quadrant in which the angle –184D 22 ' lies.
A) 3 B) 2 C) 1 D) 4
Ans: B
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.1
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Page 143
Chapter 4: Trigonometric Functions
21. Sketch the angle
A)
B)
in standard position.
D)
E)
None of these
C)
Ans: B
Learning Objective: Sketch angle in standard position
Section: 4.1
22. Determine a pair of angles (one positive and one negative) in degree measure coterminal
D
to the angle 69 .
D) 138D , −69D
A)
249D , –111D
E)
B)
249D , –291D
429D , –291D
C)
369D , –231D
Ans: B
Learning Objective: Identify angles coterminal to a given angle
Section: 4.1
Page 144
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Chapter 4: Trigonometric Functions
23. Determine two coterminal angles (one positive and one negative) for the given angle.
Give your answer in degrees.
Ans: Answers may vary. One possible response is given below.
Learning Objective: Identify angles coterminal to a given angle
Section: 4.1
24. Determine two coterminal angles (one positive and one negative) for the given angle.
Give your answer in degrees.
θ = 280°
Ans: Answers may vary. One possible response is given below.
–80°, 640°
Learning Objective: Find two angles coterminal with given angle - degree measure
Section: 4.1
25. Determine two coterminal angles (one positive and one negative) for θ = –487° .
233° , –127°
D)
A) 143° , – 217°
B)
323° , – 397°
E)
233° , – 307°
C) 143° , – 307°
Ans: D
Learning Objective: Determine two coterminal angles (degrees)
Section: 4.1
26. Find (if possible) the complement and supplement of the given angle.
49°
A) complement: 131°; supplement: 41° D) complement: 41°; supplement: 311°
B) complement: 49°; supplement: 131° E) complement: 41°; supplement: 131°
C) complement : 131°; supplement:
311°
Ans: E
Learning Objective: Identify the supplement and complement of an angle
Section: 4.1
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Page 145
Chapter 4: Trigonometric Functions
27. Rewrite the given angle in radian measure as a multiple of π . (Do not use a calculator.)
72°
7π
π
2π
3π
B) π C) 5 D) 5
E) 5
A) 5
Ans: D
Learning Objective: Convert degree measure to radian measure (multiple of pi)
Section: 4.1
28. Rewrite the given angle in radian measure as a multiple of π . (Do not use a calculator.)
–60°
2π
π
π
5π
−
−
−
−
3
A)
B) –π C) 6 D) 3 E) 18
Ans: D
Learning Objective: Convert degree measure to radian measure (multiple of pi)
Section: 4.1
29.
–
π
Rewrite the angle 3 radians in degree measure.
D
D
D
D
D
A) –120 B) –40 C) –60 D) –30 E) 120
Ans: C
Learning Objective: Convert radian measure to degree measure
Section: 4.1
30. Rewrite the given angle in degree measure. (Do not use a calculator.)
11π
−
6
A) –660° B) –300° C) –360° D) –315° E) –330°
Ans: E
Learning Objective: Convert from radian measure to degree measure
Section: 4.1
31. Convert the given angle measure from degrees to radians. Round to three decimal
places.
–124.3°
A) –2.169 B) –1.646 C) –7121.865 D) –1.085 E) –4.339
Ans: A
Learning Objective: Convert from degree measure to radian measure
Section: 4.1
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Chapter 4: Trigonometric Functions
32. Convert the given angle measure from radians to degrees. Round to three decimal
places.
3π
–
8
A) –0.021° B) –67.500° C) –135.000° D) –33.750° E) –480.000°
Ans: B
Learning Objective: Convert from radian measure to degree measure
Section: 4.1
33. Convert the given angle measure from radians to degrees. Round to three decimal
places.
–5.51
A) –0.096° B) –315.700° C) –631.399° D) –157.850° E) –10.399°
Ans: B
Learning Objective: Convert from radian measure to degree measure
Section: 4.1
34. Convert the angle measure to decimal degree form.
–159°13'
A) –158.783° B) –159.013° C) –159.217° D) –2.775° E) –9110.774°
Ans: C
Learning Objective: Convert from degree-minute measure to decimal degree
Section: 4.1
35. Convert the angle measure to decimal degree form.
–595°13' 40"
A) –594.772°
D) –10.385°
B) –595.013°
E) –34,094.025°
C) –595.228°
Ans: C
Learning Objective: Convert from degree-minute-second measure to decimal degree
Section: 4.1
36. Convert the angle measure to D°M ′S ′′ form.
–18.38°
A) –18° 22' B) –18° 22' 48" C) –18° 38' D) –18° 48' 22" E) –18° 48'
Ans: B
Learning Objective: Convert from decimal degree measure to DMS measure
Section: 4.1
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Page 147
Chapter 4: Trigonometric Functions
37. Find the angle in radians.
A)
B)
C)
D)
E)
Ans: A
Learning Objective: Calculate measure of central angle given radius and arc length
Section: 4.1
Page 148
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Chapter 4: Trigonometric Functions
38. Find the angle, in radians, in the figure below if S = 11 and r = 8 .
S
θ
r
8
11
11π
8π
19π
A) 11 B) 8 C) 8
D) 11 E) 8
Ans: B
Learning Objective: Find measure of central angle given radius and arc length
Section: 4.1
39. Find the radian measure of the central angle of the circle of radius 6 centimeters that
intercepts an arc of length 32 centimeters.
3
6
2
16
32
θ=
θ=
θ=
θ=
θ=
16 B)
5 C)
3 D)
3 E)
7
A)
Ans: D
Learning Objective: Find measure of central angle given radius and arc length
Section: 4.1
40. Find the radian measure of the central angle of a circle of radius r that intercepts an arc
of length s.
radius: r = 9 inches arc length: s = 33 inches
3
3π
11π
11
11
D) 6 E) 3
A) 11 B) 11 C) 3
Ans: E
Learning Objective: Calculate measure of central angle given radius and arc length
Section: 4.1
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Chapter 4: Trigonometric Functions
41. Find the length of the arc on a circle of radius r intercepted by a central angle θ .
19π
θ=
15
radius: r = 11 inches central arc:
D)
A)
19π
209π
inches
inches
15
15
B)
E)
209π
209
inches
inches
30
15
C)
2299π
inches
15
Ans: D
Learning Objective: Calculate arc length given angle measure and radius
Section: 4.1
42.
π
Find the radius of a circular sector with an arc length 27 feet and a central angle 6
radians. Round your answer to two decimal places.
A) 51.57 feet B) 1.43 feet C) 14.14 feet D) 0.02 foot E) 0.70 foot
Ans: A
Learning Objective: Compute radius of circle given arc length and central angle
Section: 4.1
43. A satellite in circular orbit 1125 kilometers above a planet makes one complete
revolution every 120 minutes. Assuming that the planet is a sphere of radius 6400
kilometers, compute the linear speed of the satellite in kilometers per minute. Round
your answer to the nearest whole number.
A) 22,575 kilometers per minute
D) 394 kilometers per minute
B) 3375 kilometers per minute
E) 59 kilometers per minute
C) 29 kilometers per minute
Ans: D
Learning Objective: Compute linear speed
Section: 4.1
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Chapter 4: Trigonometric Functions
44. The circular blade of a saw has a diameter of 7 inches and rotates at 2240 revolutions
per minute. Find the angular speed in radians per second.
D)
A)
784π
112π
3 radians per second
3 radians per second
14π radians per second
B)
E)
224π
3 radians per second
C)
1568π
3
radians per second
Ans: B
Learning Objective: Compute angular speed
Section: 4.1
45. The circular blade of a saw has a diameter of 9 inches and rotates at 2300 revolutions
per minute. Find the linear speed of the saw teeth in feet per second. Round your
answer to two decimal places.
A) 180.64 feet per second
D) 90.32 feet per second
B) 1083.85 feet per second
E) 240.86 feet per second
C) 14.38 feet per second
Ans: D
Learning Objective: Compute angular speed
Section: 4.1
46. Determine the exact value of sin θ .
θ
⎛ 24 7 ⎞
⎜ ,− ⎟
⎝ 25 25 ⎠
7
7
25
25
24
–
–
7
7
A) 25 B) 25 C)
D) 7 E)
Ans: A
Learning Objective: Calculate exact values of trigonometric function given point on
unit circle
Section: 4.2
–
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Page 151
Chapter 4: Trigonometric Functions
47. Determine the exact value of cot θ .
θ
⎛ − 5 , − 12 ⎞
⎜ 13 13 ⎟
⎝
⎠
5
5
12
12
–
–
5 E) 1
A) 12 B) 12 C) 5 D)
Ans: A
Learning Objective: Calculate exact values of trigonometric function given point on
unit circle
Section: 4.2
48. Find the point (x, y) on the unit circle that corresponds to the real number t.
A)
B)
C)
D)
E)
Ans: E
Learning Objective: Identify point on unit circle that corresponds to a given angle
Section: 4.2
Page 152
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Chapter 4: Trigonometric Functions
49.
t=
( x, y )
5π
.
6
on the unit circle corresponding to the real number
Find the point
A)
D)
⎛1
⎛ 1 3⎞
3⎞
⎜⎜ , –
⎟⎟
⎜⎜ – ,
⎟⎟
2 ⎠
⎝2
⎝ 2 2 ⎠
E)
B)
⎛
⎛
3 1⎞
2
2⎞
, ⎟⎟
,–
⎜⎜ –
⎜⎜ –
⎟
2 ⎟⎠
⎝ 2 2⎠
⎝ 2
C)
⎛ 3 1⎞
, – ⎟⎟
⎜⎜
2⎠
⎝ 2
Ans: B
Learning Objective: Identify point on unit circle that corresponds to a given angle
Section: 4.2
50.
t=–
5π
.
3
Evaluate the tangent of the real number
3
3
–
3
A)
B) 3
C) 3 D) – 3 E) –1
Ans: C
Learning Objective: Evaluate trigonometric function
Section: 4.2
51. Evaluate, if possible, the given trigonometric function at the indicated value.
A)
B)
C)
D)
E)
Ans: A
Learning Objective: Evaluate trigonometric function
Section: 4.2
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Page 153
Chapter 4: Trigonometric Functions
52.
t=–
11π
.
6
Find the cosecant of the real number
2 3
2 3
–
3
A) 2 B) 3
C) – 2 D)
E) –2
Ans: A
Learning Objective: Evaluate trigonometric function
Section: 4.2
53.
t=–
3π
.
4
Find the cotangent (if it exists) of the real number
⎛ 3π ⎞
2
cot ⎜ –
–
⎟
⎝ 4 ⎠ does not exist
2
B) 1 C) –1 D) 0 E)
A)
Ans: B
Learning Objective: Evaluate trigonometric function
Section: 4.2
54. Evaluate the trigonometric function using its period as an aid.
⎛ 19π ⎞
cos ⎜
⎟
⎝ 3 ⎠
1
1
3
3
2 3
–
−
2
A) 2 B) 2 C) 2
D)
E) 3
Ans: A
Learning Objective: Evaluate trigonometric function using periodicity as an aid
Section: 4.2
55. Evaluate the trigonometric function using its period as an aid.
⎛ 11π ⎞
sin ⎜ –
⎟
⎝ 3 ⎠
3
3
1
1
2 3
–
−
2
A) 2
C) 2 D) 2 E) 3
B)
Ans: A
Learning Objective: Evaluate trigonometric function using periodicity as an aid
Section: 4.2
Page 154
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Chapter 4: Trigonometric Functions
56. Evaluate the trigonometric function using its period as an aid.
⎛ 5π ⎞
cos ⎜ –
⎟
⎝ 6 ⎠
3
3
1
1
2 3
–
−
2
A)
B) 2
C) 2 D) 2 E) 3
Ans: A
Learning Objective: Evaluate trigonometric function using periodicity as an aid
Section: 4.2
57. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set in the correct angle mode.)
–π
tan
9
A) –0.0061 B) –0.3640 C) 1.0000 D) –2.7475 E) –0.3420
Ans: B
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.2
58. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set in the correct angle mode.)
sin
π
9
A) 0.0061 B) 0.9397 C) 1.0000 D) 2.9238 E) 0.3420
Ans: E
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.2
59.
sec ( 2.4 ) .
Evaluate
Round your answer to four decimal places.
A) 1.4805 B) –0.7374 C) 0.6755 D) –1.3561 E) 0.9144
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.2
60.
cot ( 23.2 ) .
Evaluate
Round your answer to four decimal places.
A) 2.6411 B) 23.1856 C) 0.0431 D) 0.3786 E) –1.0693
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.2
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Chapter 4: Trigonometric Functions
61. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set in the correct angle mode.)
tan 7.7
A) 0.1352 B) 0.9882 C) 0.1534 D) 6.4429 E) 1.0120
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.2
62. Use the figure and a straightedge to approximate the value of sin 2.25 .
A) 0.04 B) 0.78 C) –0.63 D) –1.24 E) 1.29
Ans: B
Learning Objective: Approximate the value of a trigonometric function with;
Approximate the value of a trigonometric function with a polar grid
Section: 4.2
Page 156
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Chapter 4: Trigonometric Functions
63. Use the figure and a straightedge to approximate the value of cos 2 .
A) 1.00 B) 0.91 C) –0.42 D) –2.19 E) –2.40
Ans: C
Learning Objective: Approximate the value of a trigonometric function with a polar
grid
Section: 4.2
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Page 157
Chapter 4: Trigonometric Functions
64. Use the figure and a straightedge to approximate the solution of the given equation,
where 0 ≤ t < 2π .
sin t = 0.95
A) 0.8 B) 1.3 C) 0.3, 6 D) 1.3, 1.9 E) Undefined
Ans: D
Learning Objective: Use polar grid to approximate solution of trigonometric equation
Section: 4.2
Page 158
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Chapter 4: Trigonometric Functions
65. Use the figure and a straightedge to approximate the solution of the given equation,
where 0 ≤ t < 2π .
cos t = –0.95
A) 0.6 B) 4.4 C) 2.8, 3.5 D) 4.4, 5.0 E) Undefined
Ans: C
Learning Objective: Approximate the value of a trigonometric function with a polar
grid
Section: 4.2
66. Find the exact value of the given trigonometric function of the angle θ shown in the
figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: sin θ
c
b
θ
a
b = 16, c = 34
15
8
8
15
17
A) 17 B) 17 C) 15 D) 8 E) 8
Ans: B
Learning Objective: Evaluate trigonometric function with a right triangle
Section: 4.3
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Page 159
Chapter 4: Trigonometric Functions
67. Find the exact value of the given trigonometric function of the angle θ shown in the
figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: cot θ
c
b
θ
a
b = 24, c = 51
8
15
15
8
17
A) 17 B) 17 C) 8 D) 15 E) 15
Ans: C
Learning Objective: Evaluate trigonometric function with a right triangle
Section: 4.3
68. Find the exact value of the given trigonometric function of the angle θ shown in the
figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: sin θ
c
a
θ
a
a=4
2
2
2
4
A) 4 2 B) 2 C)
D) 1 E)
Ans: C
Learning Objective: Evaluate trigonometric function with a right triangle
Section: 4.3
Page 160
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Chapter 4: Trigonometric Functions
69. Find the exact value of csc θ , using the triangle shown in the figure below, if
a = 12 and b = 5 .
c
b
θ
a
13
13
12
5
12
A) 5 B) 12 C) 5 D) 13 E) 13
Ans: A
Learning Objective: Evaluate trigonometric function with a right triangle
Section: 4.3
70.
5
7 , find sec θ .
Given that
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute
angle θ ; then use the Pythagorean Theorem to determine the third side.)
5
7
2 6
7
A) 7
B) 5 C) 2 6 D) 14 6 E) 2 6
Ans: E
Learning Objective: Compute value of a trigonometric function given another
trigonometric function
Section: 4.3
71.
3
4 , find csc θ .
Given that
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute
angle θ ; then use the Pythagorean Theorem to determine the third side.)
3
4
7
4
A) 4
B) 3 C) 7 D) 64 7 E) 7
Ans: E
Learning Objective: Compute value of a trigonometric function given another
trigonometric function
Section: 4.3
sin θ =
cos θ =
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Chapter 4: Trigonometric Functions
72. Given that tan θ = 10 , find cos θ .
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute
angle θ ; then use the Pythagorean Theorem to determine the third side.)
1
10
101
1
A) 101 B) 101 C) 101 D) 10
E) 10
Ans: A
Learning Objective: Compute value of a trigonometric function given another
trigonometric function
Section: 4.3
73.
Page 162
9
17 , find tan θ .
Given that
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute
angle θ ; then use the Pythagorean Theorem to determine the third side.)
9
17
4 13
17
A) 17
B) 9 C) 4 13 D) 68 13 E) 4 13
Ans: C
Learning Objective: Compute value of a trigonometric function given another
trigonometric function
Section: 4.3
sin θ =
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
74.
Given
sin 30 ° =
1
3
cos 30° =
2 and
2 , determine the following:
A)
B)
C)
D)
E) undefined
Ans: D
Learning Objective: Compute value of a trigonometric function given two
trigonometric values
Section: 4.3
75.
4 5
9 and sec (θ ) = 6, find cot (θ ) .
2 5
27 5
9 5
3 5
B) 27
C) 10
D) 20
E) 40
sin (θ ) =
Given
8 5
A) 3
Ans: E
Learning Objective: Compute value of a trigonometric function given two
trigonometric values
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Page 163
Chapter 4: Trigonometric Functions
76. Use the given function values and the trigonometric identities (including the cofunction
identities) to find the indicated trigonometric function.
13
2 13
csc θ =
, cos θ =
3
13 ; find sin ( 90° − θ )
3
2
3 13
1 13
2 13
A) 2 B) 3 C) 13
D) 13
E) 13
Ans: E
Learning Objective: Compute value of a trigonometric function given two
trigonometric values
Section: 4.3
77.
Given sec θ = 10 and tan θ = 3 , determine the following.
A)
B)
C)
D)
E) undefined
Ans: B
Learning Objective: Compute value of a trigonometric function given two
trigonometric values
Section: 4.3
Page 164
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
78. Using trigonometric identities, determine which of the following is equivalent to the
following expression.
A)
B)
C)
D)
E)
Ans: C
Learning Objective: Write an equivalent expression for a trig expression
Section: 4.3
79. Use trigonometric identities to transform the left side of the equation into the right side.
Assume all angles are positive acute angles, and show all of your work.
Ans:
Learning Objective: Prove trigonometric identity
Section: 4.3
80. Use a calculator to evaluate the function. Round your answers to four decimal places.
(Be sure the calculator is in the correct angle mode.)
sin 42.7°
A) –0.9587 B) 0.6968 C) 0.6782 D) 0.7349 E) 0.9228
Ans: C
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Page 165
Chapter 4: Trigonometric Functions
81. Use a calculator to evaluate the function. Round your answers to four decimal places.
(Be sure the calculator is in the correct angle mode.)
sec 41.5°
A) –1.2651 B) 0.7490 C) 1.3352 D) –0.9168 E) 0.8847
Ans: C
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
82. Use a calculator to evaluate tan 94° 48' . Round your answer to four decimal places.
A) –11.9087 B) –12.7632 C) 0.2365 D) 0.6162 E) –5.9548
Ans: A
Learning Objective: Evaluate trig values using calculator
Section: 4.3
83. Use a calculator to evaluate the function. Round your answers to four decimal places.
(Be sure the calculator is in the correct angle mode.)
csc 70°22 '
A) 0.9419 B) 1.0532 C) 1.0617 D) 2.9762 E) –1.1531
Ans: C
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
84. Use a calculator to evaluate the function. Round your answers to four decimal places.
(Be sure the calculator is in the correct angle mode.)
cot 44°14 '
A) 0.9736 B) 3.8995 C) 1.0271 D) –1.2145 E) –0.8234
Ans: C
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
85.
86.
Page 166
cos (16D 28'15'') .
Use a calculator to evaluate
Round your answer to four decimal
places.
A) –0.7229 B) 0.9577 C) 0.5150 D) 0.9590 E) 1.0428
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
⎛π ⎞
cot ⎜ ⎟ .
⎝ 3 ⎠ Round your answer to four decimal places.
Use a calculator to evaluate
A) 0.5774 B) 1.7319 C) 3.1246 D) 0.3200 E) 2.8881
Ans: A
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
87.
88.
⎛π ⎞
cot ⎜ ⎟ .
⎝ 8 ⎠ Round your answer to four decimal places.
Use a calculator to evaluate
A) 2.4142 B) 0.4142 C) 1.7926 D) 0.5578 E) 7.9583
Ans: A
Learning Objective: Evaluate Cotangent Function Using Calculator
Section: 4.3
cos θ =
3
2 , find the value of θ in degrees ( 0 < θ < 90 ° ) without the aid of a
If
calculator.
A) θ = 30 °
B) θ = 45 °
C) θ = 15 °
D) θ = 90 °
E) θ = 75°
Ans: A
Learning Objective: Compute the angle given a trigonometric function
Section: 4.3
89. Solve for y.
y
60°
5
y=
5 2
3
y=
3
5
C)
A) y = 5 3 B)
Ans: A
Learning Objective: Solve right triangle
Section: 4.3
D)
y=
5
3
E) y = 5 2
90. Use a calculator to evaluate the function. Round your answers to four decimal places.
(Be sure the calculator is in the correct angle mode.)
sin 73.3°
A) –0.8641 B) 0.5044 C) 0.9578 D) 0.2874 E) 3.3332
Ans: C
Learning Objective: Use calculator to evaluate trigonometric function
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Page 167
Chapter 4: Trigonometric Functions
91. Determine the value of x.
23
46 3
1
3
3
B) 46 C) 46 D) 46
A)
Ans: A
Learning Objective: Solve right triangle
Section: 4.3
23
E) 60
92. A 2-meter tall person walks from the base of a streetlight directly toward the tip of the
shadow cast by the streetlight. When the person is 3 meters from the base of the
streetlight and 5 meters from the tip of the streetlight's shadow, the person's shadow
begins to appear beyond the streetlight's shadow. What is the height of the streetlight?
6
16
5
5
A) 5 meters B) 5 meters C) 6 meters D) 16 meter E) 6 meter
Ans: B
Learning Objective: Apply right triangle trigonometry to solve an application
Section: 4.3
93. Solve for r.
r
45°
23
r=
23 3
2
r=
23 2
2
r=
A)
B)
C)
Ans: E
Learning Objective: Solve right triangle
Section: 4.3
Page 168
23
3
D)
r=
3
46
E) r = 23 2
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
94. Downtown Sardis City is located due north of a straight segment of train track oriented
in an east-west direction (see map below). A passenger on a train that is traveling from
west to east notes that downtown Sardis City is visible at an angle A = 45o to the left of
the tracks. After traveling a distance d = 8 kilometers, the passenger notes that the angle
to Sardis City is B = 55.5o. Estimate the distance from the track to downtown Sardis
City. Round to the nearest kilometer.
Sardis City
not drawn to scale
North
A
B
train track
d
A) 28 km B) 26 km C) 29 km D) 30 km E) 31 km
Ans: B
Learning Objective: Apply right triangle trigonometry to solve an application
Section: 4.3
95. One end of a zip-line cable is attached to the top of a 100-foot pole while the other end
is anchored at ground level to a stake exactly 100 3 feet from the base of the pole.
Find the angle of elevation of the zip-line.
100 ft
100 3 ft
D
D
D
D
D
A) 60 B) 100 3 C) 30 D) 100 E) 45
Ans: C
Learning Objective: Calculate angle of elevation
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Page 169
Chapter 4: Trigonometric Functions
96. One end of a zip-line cable is attached to the top of a 50-foot pole while the other end is
anchored at ground level to a stake exactly 80 feet from the base of the pole. How
many feet of cable are needed for the zip-line?
50 ft
80 ft
A) 130 feet B) 130 feet C) 8900 feet D) 10 89 feet E) 10 39 feet
Ans: D
Learning Objective: Solve right triangle
Section: 4.3
97. One end of a zip-line cable is attached to the top of a 45-foot pole while the other end is
anchored at ground level to a stake exactly 40 feet from the base of the pole. A person
descending the zip-line takes 5 seconds to reach the ground from the top of the pole.
What is the vertical speed, in feet per second, of the person dropping? Round your
answer to two decimal places.
45 ft
40 ft
A) 12.04 feet per second
D) 725.00 feet per second
B) 360.00 feet per second
E) 8.00 feet per second
C) 9.00 feet per second
Ans: C
Learning Objective: Compute rate of vertical descent
Section: 4.3
Page 170
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
98. A certain trolley travels a distance of d = 209 meters at an angle of approximately
a = 28D , rising to a height of h = 301.5 meters above sea level. Find the vertical rise of
the inclined plane. Round your answer to two decimal places.
A) 184.54 meters
D) 27.90 meters
B) 98.12 meters
E) 56.62 meters
C) 111.13 meters
Ans: B
Learning Objective: Apply right triangle trigonometry to solve an application
Section: 4.3
99. A certain trolley travels a distance of d = 245.5 meters at an angle of approximately
a = 29.4D , rising to a height of h = 310.5 meters above sea level. Find the elevation of
the lower end of the inclined plane. Round your answer to two decimal places.
A) 189.98 meters
D) 297.56 meters
B) 96.62 meters
E) 120.52 meters
C) 172.17 meters
Ans: A
Learning Objective: Apply right triangle trigonometry to solve an application
Section: 4.3
Copyright © Houghton Mifflin Company. All rights reserved.
Page 171
Chapter 4: Trigonometric Functions
100. A certain trolley travels a distance of d = 233 meters at an angle of approximately
a = 28.6D , rising to a height of h = 318 meters above sea level. If the trolley moves up
the hillside at a rate of 25 meters per minute, find the rate at which it rises vertically.
Round your answer to two decimal places.
A) 21.95 meters per minute
D) 1.53 meters per minute
B) 8.00 meters per minute
E) 11.97 meters per minute
C) 13.63 meters per minute
Ans: E
Learning Objective: Compute rate of vertical ascent
Section: 4.3
101.
( 6, 4 ) ,
If θ is the angle pictured, whose terminal side passes through the point
sec (θ ) .
determine the exact value of
26
13
1
13
3
A) 3
B) 3
C) 13 D) 2
E) 26
Ans: B
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
Page 172
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
102. Given the figure below, determine the value of
.
A)
B)
C)
D)
E)
Ans: C
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 173
Chapter 4: Trigonometric Functions
103. Using the figure below, determine the exact value of the given trigonometric function.
A)
B)
C)
D)
E)
Ans: D
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
Page 174
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
104.
( 7, 24 ) is on the terminal side of an angle in standard position. Determine the
The point
exact value of sec θ .
D)
A)
7
7
sec θ = −
sec θ = −
25
24
B)
E)
7
25
sec θ =
sec θ =
24
7
C)
24
sec θ =
7
Ans: E
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
105.
( –7,12 ) is on the terminal side of an angle in standard position. Determine
The point
the exact value of sin θ .
12
12
12
7
12
–
–
7 B) 193 C) 12 D) 5 E) 5
A)
Ans: B
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
106.
(10,12 ) is on the terminal side of an angle in standard position. Determine the
The point
exact value of tan θ .
6
12
6
5
6
A) 5 B) 61 C) 6 D) 11 E) 22
Ans: A
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
107.
(15,12 ) is on the terminal side of an angle in standard position. Determine the
The point
exact value of sec θ .
4
4
5
5
41
A) 5 B) 41 C) 4 D) 9 E) 5
Ans: E
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 175
Chapter 4: Trigonometric Functions
108.
( –5, –12 ) is on the terminal side of an angle in standard position. Determine
The point
the exact value of cot θ .
D)
A)
13
17
cot θ = –
cot θ =
12
5
B)
E)
1
12
cot θ =
cot θ = –
13
13
C)
5
cot θ =
12
Ans: C
Learning Objective: Evaluate trigonometric function given point on terminal side of
angle
Section: 4.4
109. State the quadrant in which θ lies.
sin(θ ) > 0 and cos(θ ) > 0
A) Quadrant III
D) Quadrant II
B) Quadrant IV
E) Quadrant I or Quadrant III
C) Quadrant I
Ans: C
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.4
110. State the quadrant in which θ lies.
cot(θ ) > 0 and sec(θ ) < 0
A) Quadrant I
D) Quadrant IV
B) Quadrant II
E) Quadrant I or Quadrant III
C) Quadrant III
Ans: C
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.4
111. State the quadrant in which θ lies if csc θ < 0 and cot θ < 0 .
A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV
Ans: D
Learning Objective: Identify the quadrant in which an angle lies
Section: 4.4
Page 176
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
112. Use the function value and constraint below to evaluate the given trigonometric
function.
Function Value
Constraint
Evaluate:
A)
B)
C)
D)
E)
Ans: A
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
113.
7
25 and tan θ < 0 .
D)
25
csc θ = –
12
E)
26
csc θ = –
23
cos θ =
Determine the exact value of csc θ when
A)
1
csc θ = –
24
B)
25
csc θ = –
24
C)
24
csc θ = –
25
Ans: B
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 177
Chapter 4: Trigonometric Functions
114. Use the function value and constraint below to evaluate the given trigonometric
function.
Function Value
Constraint
Evaluate:
tan θ = 2
cos θ > 0
csc θ
1
5
A) 5 B) –2 C) 2
D) 2 E) Undefined
Ans: C
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
115. Use the function value and constraint below to evaluate the given trigonometric
function.
Function Value
Constraint
Evaluate:
sec θ = –2
tan θ < 0
cot θ
1
1
−
−
3 D) 2 E) Undefined
A) − 3 B) 3 C)
Ans: C
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
116.
7
24 and sin θ > 0 .
D)
48
sin θ =
25
E)
23
sin θ =
24
cot θ =
Determine the exact value of sin θ when
A)
26
sin θ =
25
B)
24
sin θ =
25
C)
49
sin θ =
25
Ans: B
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
117. The terminal side of θ lies on the given line in the specified quadrant. Find the value of
the given trigonometric function of θ by finding a point on the line.
Line
Quadrant
Evaluate:
y = 10 x
cos θ
I
1
10
10
1
–
101
A) 101 B) 101 C) 10 D) 101 E)
Ans: B
Learning Objective: Evaluate trig function given line containing terminal side of angle
Section: 4.4
Page 178
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
118. The terminal side of θ lies on the line –3x – 4 y = 0 in the fourth quadrant. Find the
exact value of sin θ .
D)
A)
5
3
sin θ = –
sin θ = –
3
5
B)
E)
2
11
sin θ =
sin θ = –
5
21
C)
3
sin θ = –
2
Ans: D
Learning Objective: Evaluate trig function given line containing terminal side of angle
Section: 4.4
119. The terminal side of θ lies on the given line in the specified quadrant. Find the value of
the given trigonometric function of θ by finding a point on the line.
Line
Quadrant
Evaluate:
13 x + 2 y = 0
csc θ
IV
13
13
173
173
13
–
–
–
173 C)
13
2
B)
D) 173 E)
A) 13
Ans: C
Learning Objective: Evaluate trig function given line containing terminal side of angle
Section: 4.4
120.
sec ( –4π ) .
Determine the exact value, if it exists, of
3
3
–
2
B) 1 C) 2
D) –1 E) The value does not exist.
A)
Ans: B
Learning Objective: Evaluate trigonometric function of a quadrant angle
Section: 4.4
121.
3π
Determine the exact value of the tangent of the quadrant angle 2 .
3
2
1
D) 2
E) 2
A) undefined B) 0 C) 2
Ans: A
Learning Objective: Evaluate trigonometric function of a quadrant angle
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 179
Chapter 4: Trigonometric Functions
122. Determine the exact value of the sine of the quadrant angle π .
2
3
1
–
–
2
2
C)
D) 0 E) 2
A) 1 B)
Ans: D
Learning Objective: Evaluate trigonometric function of a quadrant angle
Section: 4.4
123. Find the reference angle θ ′ for the given angle θ .
θ = 272°
A) 178° B) –182° C) 98° D) 88° E) 78°
Ans: D
Learning Objective: Calculate reference angle for given angle
Section: 4.4
124. Find the reference angle θ ′ for the given angle θ .
θ = –258°
168
° B) –12° C) 88° D) 78° E) 68°
A)
Ans: D
Learning Objective: Calculate reference angle for given angle
Section: 4.4
125. Find the reference angle θ ′ for the given angle θ .
A)
B)
C)
D)
E)
Ans: B
Learning Objective: Calculate reference angle for given angle
Section: 4.4
Page 180
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
126. Find the reference angle for the angle –191D.
D
D
D
D
D
B) 281
C) 11
D) –11
E) –281
A) 551
Ans: C
Learning Objective: Calculate reference angle for given angle
Section: 4.4
127. Find the reference angle for the angle –0.7 radians. Round your answer to one decimal
place.
A) 2.4 B) –0.7 C) –2.4 D) 0.7 E) –5.6
Ans: D
Learning Objective: Calculate reference angle for given angle
Section: 4.4
128. Evaluate the tangent of the angle without using a calculator.
–120°
3
3
1
–
3
A) 3 B)
C) 3
D) 2 E) 0
Ans: A
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
129.
cos ( – 495° )
.
Determine the exact value of
5
2
2
–
–
2
2
B) 2
C)
D) –1 E) 1
A)
Ans: C
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
130. Evaluate the sine of the angle without using a calculator.
30°
2
2
3
1
–
2
A) 2
B)
C) 2
D) 2 E) 0
Ans: D
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 181
Chapter 4: Trigonometric Functions
131. Evaluate the cosine of the angle without using a calculator.
330°
2
2
3
1
–
2
A) 2
B)
C) 2
D) 2 E) 0
Ans: C
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
132. Evaluate the sine of the angle without using a calculator.
3π
–
4
2
2
3
1
–
–
–
2
2
A)
B) 2
C)
D) 2 E) 0
Ans: A
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
133. Evaluate the sine of the angle without using a calculator.
π
3
2
3
3
1
–
2
A) 2
B)
C) 2
D) 2 E) 0
Ans: C
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
134. Evaluate the tangent of the angle without using a calculator.
–
π
6
3
3
1
–
–
2
3
A)
B)
C) – 3 D) 2 E) 0
Ans: B
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
–
Page 182
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
135. Evaluate the cosine of the angle without using a calculator.
7π
–
3
2
3
3
1
–
2
A) 2
B)
C) 2
D) 2 E) 0
Ans: D
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
136.
⎛ 13π ⎞
cos ⎜ –
⎟.
⎝ 6 ⎠
Find the exact value of
3
3
1
1
2
–
–
2
B)
C) 2 D) 2 E) 2
A) 2
Ans: A
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
137.
⎛ 20π ⎞
tan ⎜
⎟.
⎝ 3 ⎠
Find the exact value of
3
3
3
3
–
–
2
3
B) – 3 C) 2
D)
E) 3
A)
Ans: B
Learning Objective: Evaluate sine/cosine/tangent without a calculator
Section: 4.4
138. Find the indicated trigonometric value in the specified quadrant.
Function Quadrant Trigonometric Value
2
3
2
−
B) 3
sin θ =
II
cos θ
5
5
5
−
−
2
3
A) 3
C)
D)
E) Undefined
Ans: D
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
Copyright © Houghton Mifflin Company. All rights reserved.
Page 183
Chapter 4: Trigonometric Functions
139. Find the indicated trigonometric value in the specified quadrant.
Function
4
3
7
4
csc θ = −
Quadrant Trigonometric Value
III
tan θ
3
4
3
A) 7 B)
C) 7 D) 4 E) Undefined
Ans: A
Learning Objective: Evaluate trigonometric function given constraints
Section: 4.4
140. Find the indicated trigonometric value in the specified quadrant.
Function
13
11
4 3
B) 13
csc θ = −
Quadrant Trigonometric Value
IV
sec θ
11
13
11
A) 4 3
C) 4 3 D) 13 E) Undefined
Ans: C
Learning Objective: Find value of trig function given another trig value and quadrant
Section: 4.4
141. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set to the correct angle mode.)
sin ( –317° )
A) 0.7314 B) –0.2963 C) 0.9374 D) 0.6820 E) 0.9325
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
142. Use a calculator to evaluate cos 95° . Round your answer to four decimal places.
A) 0.7302 B) –0.0872 C) –0.5872 D) 0.0186 E) –0.0198
Ans: B
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
Page 184
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Chapter 4: Trigonometric Functions
143. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set to the correct angle mode.)
csc ( –348° )
A) 1.0223 B) 0.2079 C) –1.4557 D) 4.8097 E) 4.7046
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
144. Use a calculator to evaluate sec1.5 . Round your answer to four decimal places.
A) 5.5458 B) 13.3868 C) 14.1368 D) 1.0003 E) 1.5003
Ans: C
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
145. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set to the correct angle mode.)
cot ( –1.3)
A) –44.0661 B) –3.6021 C) –1.0378 D) –0.2776 E) 0.7714
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
146. Use a calculator to evaluate the trigonometric function. Round your answer to four
decimal places. (Be sure the calculator is set to the correct angle mode.)
⎛ 3π ⎞
sec ⎜ ⎟
⎝ 5 ⎠
A) 1.0005 B) 1.0515 C) 1.2116 D) –3.2361 E) –0.3249
Ans: D
Learning Objective: Evaluate trigonometric function with a calculator
Section: 4.4
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Page 185
Chapter 4: Trigonometric Functions
147. Given the equation below, determine two solutions such that 0° ≤ θ < 360° .
A)
B)
C)
D)
E)
Ans: B
Learning Objective: Solve trigonometric equation
Section: 4.4
148. Given the equation below, determine two solutions such that 0 ≤ θ < 2π .
A)
B)
C)
D)
E)
Ans: D
Learning Objective: Solve trigonometric equation
Section: 4.4
Page 186
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Chapter 4: Trigonometric Functions
149. Find two solutions of the equation in the interval [0°,360°) . Give your answers in
degrees.
A)
B)
C)
D)
E)
Ans: A
Learning Objective: Solve trigonometric equation
Section: 4.4
150. A biologist studying the habits of African wildebeests discovers that the number of
animals visiting a watering hole per hour can be modeled by
⎛ πt ⎞
⎛ πt ⎞
N ( t ) = 42 + 10 cos ⎜ ⎟ + 29 cos ⎜ ⎟
⎝ 12 ⎠
⎝ 6 ⎠,
where N(t) is the number of animals per hour and t is the time in hours after midnight
(12:00 A.M. corresponds to t = 0). Estimate the number of wildebeests that visit the
watering hole during the 1:00 P.M. hour. Round to the nearest integer. [Note that 1 P.M.
corresponds to t = 13.]
A) 57 wildebeests
D) 23 wildebeests
B) 30 wildebeests
E) 54 wildebeests
C) 15 wildebeests
Ans: A
Learning Objective: Evaluate a trigonometric function for an application
Section: 4.4
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Page 187
Chapter 4: Trigonometric Functions
151. A submarine, cruising at a depth d = 35 meters, is on a trajectory that passes directly
below a ship (see figure). If θ is the angle of depression from the ship to the submarine,
find the distance L from the ship to the sub when θ = 50° . Round to the nearest meter.
θ
d
L
not drawn to scale
A) L = 0 meters
D) L = 54 meters
E) L = 29 meters
B) L = 133 meters
C) L = 46 meters
Ans: C
Learning Objective: Solve right triangle for an application
Section: 4.4
Page 188
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Chapter 4: Trigonometric Functions
152.
Find the period of
y = 6sin ( 3 x ) .
6
4π
3
2π
B) 6
2π
D) 3
A) 3
C) 6π
E) 6
Ans: D
Learning Objective: Calculate period of a trigonometric graph
Section: 4.5
153.
π
⎛ 7x ⎞
cos ⎜ ⎟ .
4
⎝ 2 ⎠
Find the amplitude of
π
4π
7
1
π
−
C) 2 D) 4 E) 4
A) 4 B) 7
Ans: E
Learning Objective: Identify amplitude of a trigonometric function
Section: 4.5
y=−
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Page 189
Chapter 4: Trigonometric Functions
154. Describe the relationship between f ( x) = cos( x) and g ( x) = cos 3x – 11 . Consider
amplitude, period, and shifts.
A) The period of g(x) is three times the period of f(x).
Graph of g(x) is shifted downward 11 unit(s) relative to the graph of f(x).
B)
The amplitude of g(x) is three times the amplitude of f(x).
Graph of g(x) is shifted downward 11 unit(s) relative to the graph of f(x).
C)
The period of g(x) is three times the period of f(x).
Graph of g(x) is shifted upward 11 unit(s) relative to the graph of f(x).
D)
The amplitude of g(x) is three times the amplitude of f(x).
Graph of g(x) is shifted upward 11 unit(s) relative to the graph of f(x).
E)
The period of g(x) is eleven times the period of f(x).
Graph of g(x) is shifted downward 3 unit(s) relative to the graph of f(x).
Ans: A
Learning Objective: Explain the relationship between two trigonometric functions
Section: 4.5
Page 190
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Chapter 4: Trigonometric Functions
155.
Determine the graph of
6
A)
y = 6sin ( x ) .
4π
B)
6
4π
C)
1
2π
3
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Page 191
Chapter 4: Trigonometric Functions
D)
1
2π
3
E)
6
4π
Ans: B
Learning Objective: Graph trigonometric function
Section: 4.5
Page 192
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Chapter 4: Trigonometric Functions
156.
1
y = cos ( x ) .
9
Determine the graph of
9
A)
4π
B)
9
4π
C)
1
9
4π
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Page 193
Chapter 4: Trigonometric Functions
D)
1
9
4π
E)
9
4π
Ans: C
Learning Objective: Graph trigonometric function
Section: 4.5
Page 194
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Chapter 4: Trigonometric Functions
157.
⎛ 5x ⎞
Determine the graph of y = cos ⎜ ⎟ .
⎝ 3 ⎠
A)
1
12π
5
B)
5
3
4π
C)
1
20π
3
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Page 195
Chapter 4: Trigonometric Functions
D)
1
20π
3
E)
5
3
12π
5
Ans: A
Learning Objective: Graph trigonometric function
Section: 4.5
Page 196
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Chapter 4: Trigonometric Functions
158. Sketch the graph of the function below, being sure to include at least two full periods.
A)
B)
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Page 197
Chapter 4: Trigonometric Functions
C)
D)
E)
Ans: C
Learning Objective: Graph trigonometric function
Section: 4.5
Page 198
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Chapter 4: Trigonometric Functions
159. Sketch the graph of the function below, being sure to include at least two full periods.
A)
B)
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Page 199
Chapter 4: Trigonometric Functions
C)
D)
E)
Ans: E
Learning Objective: Sketch graph of trig function
Section: 4.5
Page 200
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Chapter 4: Trigonometric Functions
160.
⎛πx ⎞
Determine the period of y = –3 – 3cos ⎜
⎟.
⎝ 9 ⎠
2π
2
A) 18 B)
C) 9 D) 15 E)
9
9
Ans: A
Learning Objective: Identify the period of a trigonometric function
Section: 4.5
161.
⎛πx ⎞
Determine the amplitude of y = –3 – 4 cos ⎜
⎟.
⎝ 8 ⎠
A) –4 B) –7 C) 4 D) –3 E) 3
Ans: C
Learning Objective: Identify the amplitude of a trigonometric function
Section: 4.5
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Page 201
Chapter 4: Trigonometric Functions
162. Determine the period and amplitude of the following function.
A)
B)
C)
D)
E)
Ans: D
Learning Objective: Identify the amplitude and period of a trigonometric function
Section: 4.5
163.
Page 202
⎛x π⎞
Determine the period and amplitude of y = –2 cos ⎜ + ⎟ .
⎝9 2⎠
A)
D)
2π
π
period:
; amplitude: 2
period: ; amplitude: –2
9
9
E)
B) period: 18π ; amplitude: 2
2π
period: –
; amplitude: 2
9
C) period: 9π ; amplitude: –4
Ans: B
Learning Objective: Determine period and amplitude of trig function
Section: 4.5
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Chapter 4: Trigonometric Functions
164. Find a and d for the function f ( x) = a sin x + d such that the graph of f ( x) matches the
graph below.
A)
B)
C)
D)
E)
Ans: B
Learning Objective: Solve for values of a and d of a trig function from a graph
Section: 4.5
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Page 203
Chapter 4: Trigonometric Functions
165. Find a, b, and c for the function f ( x) = a cos ( bx − c ) such that the graph of f ( x)
matches the graph below.
A)
B)
C)
D)
E)
Ans: C
Learning Objective: Solve for values of a and d of a trig function from a graph
Section: 4.5
Page 204
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Chapter 4: Trigonometric Functions
166. The percent y (in decimal form) of the moon's face that is illuminated on day x of a
certain year is shown in the chart. Find a trigonometric model for the data. Round all
numeric values to one decimal.
Day, x Percent, y
33
0.5
40
0.0
48
0.5
55
1.0
63
0.5
70
0.0
A)
y = 0.5cos ( 0.1x + 2.3) − 0.5
D)
B)
E)
C)
y = 2.0 cos ( 0.2 x − 11.0 ) + 0.5
y = 0.5cos ( 0.1x − 2.3) − 0.5
y = 0.5cos ( 0.2 x − 11.0 ) + 0.5
y = 2.0 cos ( 0.2 x − 11.0 ) − 0.5
Ans: D
Learning Objective: Model data with a trigonometric function
Section: 4.5
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Page 205
Chapter 4: Trigonometric Functions
167.
1
Determine the graph of y = tan ( x ) .
3
−π
π
A)
y
x
B)
−
π
6
π
y
6
x
C)
−
π
2
π
y
2
x
Page 206
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Chapter 4: Trigonometric Functions
D)
−
π
2
π
y
2
x
E)
−
π
6
π
y
6
x
Ans: C
Learning Objective: Graph tangent function
Section: 4.6
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Page 207
Chapter 4: Trigonometric Functions
168. Determine the graph of y = –3 tan ( 6 x ) .
−12π
12π
A)
y
x
B)
−
π
3
π
y
3
x
C)
−
π
12
π
y
12
x
Page 208
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Chapter 4: Trigonometric Functions
D)
−
π
6
π
y
6
x
E)
−
π
12
π
y
12
x
Ans: E
Learning Objective: Graph tangent function
Section: 4.6
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Page 209
Chapter 4: Trigonometric Functions
169. Which of the following functions is represented by the graph below?
A)
B)
C)
D)
E)
Ans: D
Learning Objective: Graph tan/csc/sec functions
Section: 4.6
Page 210
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Chapter 4: Trigonometric Functions
170. Use a graphing utility to graph the function below, making sure to show at least two
periods.
A)
B)
C)
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Page 211
Chapter 4: Trigonometric Functions
D)
E)
Ans: B
Learning Objective: Graph tan/csc/sec functions
Section: 4.6
Page 212
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Chapter 4: Trigonometric Functions
171.
1
⎛ x⎞
Determine the graph of y = cot ⎜ ⎟ .
6
⎝5⎠
−6π
6π
A)
y
x
B)
−
π
5
π
y
5
x
C)
−6π
y
6π
x
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Page 213
Chapter 4: Trigonometric Functions
D)
−5π
y
5π
x
E)
−5π
y
5π
x
Ans: D
Learning Objective: Graph tan/csc/sec functions
Section: 4.6
Page 214
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Chapter 4: Trigonometric Functions
172. Use a graphing utility to graph the expression below, making sure to show at least two
periods.
A)
B)
C)
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Chapter 4: Trigonometric Functions
D)
E)
Ans: A
Learning Objective: Graph tan/csc/sec functions
Section: 4.6
173. Approximate the solution to the equation tan ( x ) = –1 , where −π < x ≤ π , by graphing.
Round your answer to one decimal.
A) –0.8, 0.8 B) –0.8, 2.4 C) 0.8, –2.4 D) 2.4, –2.4 E) 2.4, 0.8
Ans: B
Learning Objective: Solve trigonometric equation by graphing
Section: 4.6
Page 216
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Chapter 4: Trigonometric Functions
174. Use the graph shown below to determine if the function is even, odd, or neither.
A) even B) odd C) neither
Ans: B
Learning Objective: Identify a trigonometric function as even, odd, or neither
Section: 4.6
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Page 217
Chapter 4: Trigonometric Functions
175. Determine which of the graphs below represents
.
A)
B)
C)
Page 218
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Chapter 4: Trigonometric Functions
D)
E)
Ans: D
Learning Objective: Graph damped trigonometric functions
Section: 4.6
176.
⎛ 2⎞
Determine the exact value of arcsin ⎜⎜
⎟⎟ .
2
⎝
⎠
A)
π
B)
π
C) –
π
D) –
π
π
E)
4
6
4
3
6
Ans: A
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
177. Determine the exact value of arcsin ( 0.5 ) .
A) –
π
B) 0
C)
π
D) –
π
E)
π
6
3
6
3
Ans: C
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
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Page 219
Chapter 4: Trigonometric Functions
178.
⎛ 3⎞
Determine the exact value of arccos ⎜⎜
⎟⎟ .
2
⎝
⎠
π
2π
π
π
3π
A)
B)
C)
D)
E)
3
4
6
3
4
Ans: A
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
179. Determine the exact value of cos −1 (1) .
A) π
B)
π
C) –
4
π
D) 0 E)
2
π
2
Ans: D
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
180.
3
without using a calculator.
3
π
3π
π
π
B)
C) −
D)
E)
4
6
3
4
Evaluate arctan
A) −
π
6
Ans: D
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
181. Determine the exact value of arctan ( –1) .
A)
π
B) –
π
C) –
π
D) 0 E)
π
2
4
4
2
Ans: C
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
182.
⎛ 2⎞
Determine the exact value of sin −1 ⎜⎜
⎟⎟ .
⎝ 2 ⎠
A)
π
B)
π
C)
π
D)
π
E) –
π
4
2
4
3
6
Ans: B
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
Page 220
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Chapter 4: Trigonometric Functions
183. Use a calculator to evaluate arctan 0.90 . Round your answer to two decimal places.
A) 1.12 B) 0.45 C) 0.62 D) 0.73 E) 1.26
Ans: D
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
184. Approximate sin −1 ( –0.84 ) . Round your answer to four decimal places.
A) –1.0027 B) –1.3429 C) –0.7446 D) –0.9973 E) –0.9285
Ans: D
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
185. Approximate tan −1 (15.5 ) . Round your answer to four decimal places.
A) 1.5064 B) 0.0646 C) –0.2110 D) 0.6638 E) –4.7390
Ans: A
Learning Objective: Evaluate an inverse trigonometric function
Section: 4.7
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Page 221
Chapter 4: Trigonometric Functions
186. Use an inverse function to write θ as a function of x.
A)
B)
C)
D)
E)
Ans: C
Learning Objective: Write an angle as a function of x using an inverse trig function
Section: 4.7
187. Use the properties of inverse trigonometric functions to evaluate cos ⎡arccos ( 0.2 ) ⎤ .
⎣
⎦
A) –0.24 B) 0.24 C) –0.1 D) 0.43 E) 0.2
Ans: E
Learning Objective: Evaluate inverse trig functions
Section: 4.7
188.
Page 222
⎡ ⎛ 3π
Use the properties of inverse trigonometric functions to evaluate arccos ⎢ cos ⎜
⎣ ⎝ 5
2π
3π
5π
3π
π
B)
C)
D)
E)
A) –
5
5
2
3
5
Ans: D
Learning Objective: Evaluate inverse trig functions
Section: 4.7
⎞⎤
⎟⎥ .
⎠⎦
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Chapter 4: Trigonometric Functions
189. Find the exact value of the expression below.
A) –
π
B) –
π
C)
π
⎡ ⎛ 7π
arctan ⎢ tan ⎜
⎣ ⎝ 6
7π
π
D)
E)
6
3
⎞⎤
⎟⎥
⎠⎦
6
3
6
Ans: C
Learning Objective: Evaluate inverse trig functions
Section: 4.7
190. Find the exact value of the expression below.
⎡ ⎛ 7π ⎞ ⎤
sin −1 ⎢sin ⎜
⎟⎥
⎣ ⎝ 2 ⎠⎦
π
7π
D)
E) –
2
2
7π
π
B) –π C) –
2
2
Ans: C
Learning Objective: Evaluate inverse trig functions
Section: 4.7
A)
191.
3⎞
⎛
Find the exact value of sin ⎜ arctan ⎟ .
4⎠
⎝
3
8
3
3
4
A)
B)
C)
D)
E)
4
5
5
8
3
Ans: C
Learning Objective: Calculate the exact value of an expression with inverse
trigonometric functions
Section: 4.7
192.
3⎞
⎛
Find the exact value of cos ⎜ sin −1 ⎟ .
5⎠
⎝
3
9
5
4
4
A)
B)
C)
D)
E)
5
5
3
9
5
Ans: E
Learning Objective: Calculate the exact value of an expression with inverse
trigonometric functions
Section: 4.7
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Page 223
Chapter 4: Trigonometric Functions
193. Find the exact value of the expression below.
⎡
⎛ 5 ⎞⎤
sec ⎢arctan ⎜ − ⎟ ⎥
⎝ 12 ⎠ ⎦
⎣
12
13
D) −
E) −
13
12
12
13
12
C)
B)
5
12
13
Ans: B
Learning Objective: Calculate the exact value of an expression with inverse
trigonometric functions
Section: 4.7
A) −
194.
x⎞
⎛
Write an algebraic expression that is equivalent to sin ⎜ arctan ⎟ .
3⎠
⎝
3
A)
B)
3
x
C)
x2 + 9
x
D)
x2 + 9
3
E)
x
x2 + 9
x2 + 9
Ans: E
Learning Objective: Rewrite inverse trig expression as an algebraic expression
Section: 4.7
195. Write an algebraic expression that is equivalent to tan ( arccos 2x ) .
A)
1
2x
B)
1 − 4 x2
2x
C)
1 − 4 x2
D)
1
2
E) 2x
1 − 4x
Ans: B
Learning Objective: Rewrite inverse trig expression as an algebraic expression
Section: 4.7
196. Which of the following can be inserted to make the statement true?
arccos
16 − x 2
= arcsin ( ________ ) , 0 ≤ x ≤ 4
4
x
32 − x 2
x2
B)
C) 16 − x 2 D)
E) x
x
4
4
Ans: B
Learning Objective: Write equivalent expressions involving inverse trig functions
Section: 4.7
A)
Page 224
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Chapter 4: Trigonometric Functions
197. If B = 61° and a = 8 , determine the value of b. Round to two decimal places.
B
c
a
C
b
A
A) 14.43 B) 7.00 C) 3.88 D) 16.50 E) 4.43
Ans: A
Learning Objective: Solve for a side of a right triangle
Section: 4.8
198. In the triangle shown, if B = 62D and b = 14 , find c. Round your answer to two
decimals.
A) 15.86 B) 12.36 C) –18.94 D) 29.82 E) 6.57
Ans: A
Learning Objective: Solve for a side of a right triangle
Section: 4.8
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Page 225
Chapter 4: Trigonometric Functions
199. If a = 12 and c = 21 , determine the value of B. Round to two decimal places.
B
c
a
C
A
b
A) 29.74° B) 60.26° C) 34.85° D) 55.15° E) 39.85°
Ans: D
Learning Objective: Solve for a side of a right triangle
Section: 4.8
200. Find the altitude of the isosceles triangle shown below if θ = 42 ° and b = 10 feet .
Round answer to two decimal places.
θ
θ
b
B) 1.92 feet
C) 3.35 feet D) 4.50 feet E) 5.55 feet
A) 9.00 feet
Ans: D
Learning Objective: Solve for the altitude of an isosceles triangle
Section: 4.8
201. A ladder of length 15 feet leans against the side of a building. The angle of elevation of
the ladder is 70D. Find the distance from the top of the ladder to the ground. Round
your answer to two decimals.
A) 5.46 feet B) 14.10 feet C) 5.13 feet D) 9.50 feet E) 11.61 feet
Ans: B
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
Page 226
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Chapter 4: Trigonometric Functions
202. From a point 45 feet in front of a church, the angles of elevation to the base of the
steeple and the top of the steeple are 35D and 46D 20 ', respectively. Find the height of
the steeple. Round your answer to two decimals.
A) 47.14 feet B) 31.51 feet C) 69.56 feet D) 42.95 feet E) 15.64 feet
Ans: E
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
203. A communications company erects a 83-foot tall cellular telephone tower on level
ground. Determine the angle of depression, θ (in degrees), from the top of the tower to
a point 45 feet from the base of the tower. Round answer to two decimal places.
A) 44.53° B) 53.03° C) 61.53° D) 32.52° E) 57.52°
Ans: C
Learning Objective: Calculate angle of depression
Section: 4.8
204. A certain satellite orbits 12, 000 miles above Earth's surface (see figure). Find the angle
of depression α from the satellite to the horizon. Assume the radius of the Earth is
4000 miles. Round your answer to the nearest hundredth of a degree.
12, 000 mi
satellite
α
A) 14.48 D B) 19.47 D C) 70.53 D D) 75.52 D
Ans: D
Learning Objective: Calculate angle of depression
Section: 4.8
E) 14.04 D
205. When an airplane leaves the runway, its angle of climb is 16D and its speed is 300 feet
per second. Find the plane's altitude relative to the runway in feet after 1 minute.
Round your answer to the nearest foot.
A) 3969 feet B) 2977 feet C) 6945 feet D) 4961 feet E) 5953 feet
Ans: D
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
Copyright © Houghton Mifflin Company. All rights reserved.
Page 227
Chapter 4: Trigonometric Functions
206. After leaving the runway, a plane's angle of ascent is 20° and its speed is 266 feet per
second. How many minutes will it take for the airplane to climb to a height of 13,000
feet? Round answer to two decimal places.
A) 0.81 minutes
D) 1.36 minutes
B) 2.38 minutes
E) 1.87 minutes
C) 0.89 minutes
Ans: B
Learning Objective: Compute rate of ascent
Section: 4.8
207. A sign next to the highway at the top of Saura Mountain states that, for the next 6 miles,
the grade is 9%. Determine the change in elevation (in feet) over the 6 miles for a
vehicle descending the mountain. Round answer to nearest foot.
A) –2840 feet B) –2851 feet C) –2845 feet D) –2439 feet E) –2642 feet
Ans: A
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
208. A ship leaves port at noon and has a bearing of S 27D W. The ship sails at 25 knots.
How many nautical miles south will the ship have traveled by 4 : 00 P.M.? Round your
answer to two decimals.
A) 45.40 nautical miles
D) 13.17 nautical miles
B) 25.84 nautical miles
E) 50.95 nautical miles
C) 89.10 nautical miles
Ans: C
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
209. A jet is traveling at 650 miles per hour at a bearing of 47 ° . After flying for 1.4 hours in
the same direction, how far east will the plane have traveled? Round answer to nearest
mile.
A) 849 miles east
D) 682 miles east
B) 621 miles east
E) 666 miles east
C) 205 miles east
Ans: E
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
Page 228
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
210. A land developer wants to find the distance across a small lake in the middle of his
proposed development. The bearing from A to B is N 27 ° W . The developer leaves
point A and travels 58 meters perpendicular to AB to point C. The bearing from C to
point B is N 63 ° W . Determine the distance, AB , across the small lake. Round distance
to nearest meter.
B
C
A
A) 55 meters B) 62 meters C) 80 meters D) 95 meters E) 110 meters
Ans: C
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
211. A plane is 57 miles west and 42 miles north of an airport. The pilot wants to fly directly
to the airport. What bearing should the pilot take? Answer should be given in degrees
and minutes.
A) 126 ° 23' B) 124 ° 25' C) 129 ° 20 ' D) 127 ° 22 ' E) 53 ° 37 '
Ans: A
Learning Objective: Apply trigonometry to find bearings
Section: 4.8
212. A plane is 125 miles south and 45 miles west of an airport. The pilot wants to fly
directly to the airport. What bearing should be taken? Round your answer to the
nearest degree.
A) 340 D B) 70 D C) 200 D D) 160 D E) 20 D
Ans: E
Learning Objective: Apply trigonometry to find bearings
Section: 4.8
Copyright © Houghton Mifflin Company. All rights reserved.
Page 229
Chapter 4: Trigonometric Functions
213. While traveling across the flat terrain of Nevada, you notice a mountain directly in front
of you. You calculate that the angle of elevation to the peak is 4° , and after you drive
6 miles closer to the mountain it is 5° . Approximate the height of the mountain peak
above your position. Round your answer to the nearest foot.
A) 9802 feet B) 10497 feet C) 11036 feet D) 11818 feet E) 13492 feet
Ans: C
Learning Objective: Apply trigonometry to solve an application
Section: 4.8
214. If the sides of a rectangular solid are as shown, and s = 6 , determine the angle, θ ,
between the diagonal of the base of the solid and the diagonal of the solid. Round
answer to two decimal places.
s
θ
s
2s
A) 17.21° B) 19.86° C) 21.91° D) 24.09°
Ans: D
Learning Objective: Solve for an angle in a solid
Section: 4.8
E) 26.28°
215. Find a model for simple harmonic motion d, in centimeters, with respect to time t, in
seconds, with an initial displacement (t=0) of 0 centimeters, an amplitude of 6
centimeters, and a period of 5 seconds.
A)
D)
d = 6 cos (10π t )
⎛ 2π t ⎞
d = 12 cos ⎜
⎟
⎝ 5 ⎠
E)
B)
⎛ 2π t ⎞
⎛ πt ⎞
d = 6sin ⎜
d = 3cos ⎜ ⎟
⎟
⎝ 5 ⎠
⎝ 5 ⎠
C)
⎛ πt ⎞
d = 6sin ⎜ ⎟
⎝ 5 ⎠
Ans: B
Learning Objective: Model simple harmonic motion
Section: 4.8
Page 230
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 4: Trigonometric Functions
216. Find the maximum displacement for the simple harmonic motion d, in centimeters, with
respect to time t, in seconds, described by the function below.
d = 7 cos ( 4π t )
A) 7
B)
2π
7
C) 4
D)
1
2
E) 4π
Ans: A
Learning Objective: Describe simple harmonic motion
Section: 4.8
217. Find the frequency of the simple harmonic motion described by the function below.
d = 3cos ( 8π t )
A) 4
B)
2π
3
C) 8π
D)
2
3
E) 3
Ans: A
Learning Objective: Describe simple harmonic motion
Section: 4.8
218. The displacement from equilibrium of an oscillating weight suspended by a spring is
given by y (t ) = 2 cos 6t , where y is the displacement in centimeters and t is the time in
seconds. Find the displacement when t = 1.45 , rounding answer to four decimal places.
A) 2.7845 cm
D) –3.6205 cm
B) –1.4973 cm
E) 1.4460 cm
C) –5.8257 cm
Ans: B
Learning Objective: Describe simple harmonic motion
Section: 4.8
219. For the simple harmonic motion described by the function d = 7 cos (10π t ) , find the
least positive value of t for which d = 0.
1
3
1
π
1
E)
A)
B)
C)
D)
5
20
20
10
5
Ans: A
Learning Objective: Describe simple harmonic motion
Section: 4.8
Copyright © Houghton Mifflin Company. All rights reserved.
Page 231