Solution Manual for Trigonometry, 2nd Edition

Name: Solution Manual for Trigonometry, 2nd Edition
Brand: Academic Documents Platform
Price: 15 USD
Availability: InStock
Author: Owen Collins

Get the textbook answers you need with Solution Manual for Trigonometry, 2nd Edition, an essential guide to solving textbook problems.

Owen Collins

Contributor

4.7

4 months ago

Preview (16 of 495)

SOLUTIONS MANUAL
DANIEL S. MILLER
Niagara County Community College
TRIGONOMETRY
SECOND EDITION
Robert Blitzer
Miami Dade College

iii
TABLE OF CONTENTS
TRIGONOMETRY 2E
Chapter 1 Angles and the Trigonometric Functions ...................................................................1
Chapter 2 Graphs of the Trigonometric Functions; Inverse Trigonometric Functions.............55
Chapter 3 Trigonometric Identities and Equations..................................................................175
Chapter 4 Laws of Sines and Cosines; Vectors.......................................................................297
Chapter 5 Complex Numbers, Polar Coordinates, and Parametric Equations ........................371

Chapter 1
Angles and the Trigonometric Functions
1
Section 1.1
Check Point Exercises
1. The radian measure of a central angle is the length of
the intercepted arc, s, divided by the circle’s radius, r.
The length of the intercepted arc is 42 feet: s = 42
feet. The circle’s radius is 12 feet: r = 12 feet. Now
use the formula for radian measure to find the radian
measure of .
θ
42 feet 3.5
12 feet
s
r
θ = = =
Thus, the radian measure of
θ is 3.5
2. a. radians 60
60 60 radians
180 180
radians
3
π
π
π
° = ° ⋅ =
°
=
b. radians 270
270 270 radians
180 180
3 radians
2
π
π
π
° = ° ⋅ =
°
=
c. radians 300
300 300 radians
180 180
5 radians
3
π
π
π
−
− ° = − ° ⋅ =
°
= −
3. a.
oradians 180
radians 4 radians
π
π π
= ⋅
4
o180 o45
4
= =
b.
o4 4 radians 180
radians
π
π π
− = − ⋅
3 3
o4 180 o240
3
⋅
= − = −
c.
o180
6 radians 6 radians radians
π
= ⋅
o6 180 o343.8
π
⋅
= ≈
d.
o180
4.7 radians 4.7 radians radians
π
− = − ⋅
o4.7 180 o269.3
π
− ⋅
= ≈ −
4. a.
b.
c.
d.
5. a. For a 400º angle, subtract 360º to find a positive
coterminal angle.
400 o – 360 o = 40 o
b. For a –135º angle, add 360º to find a positive
coterminal angle.
–135 o + 360 o = 225 o
6. a. 13 13 10 3
2
5 5 5 5
π
π π π
π− = − =
b. 30 29
2
15 15 15 15
π
π π π
π− + = − + =

Chapter 1 Angles and the Trigonometric Functions
2
7. a. 855 360 2 855 720 135° − ° ⋅ = ° − ° = °
b. 17 17
2 2 4
3 3
π
π
π
π− ⋅ = −
17 12 5
3 3 3
π π π
= − =
c. 25 25
2 3 6
6 6
π
π
π
π− + ⋅ = − +
25 36 11
6 6 6
π π π
= − + =
d. ( )17.4 17.4 57 991.8≈ = 
For a 991.8 angle, we need to subtract two
multiples of 360 to find a positive coterminal
angle less than 360 .
17.4 2 2 17.4 4 4.8
π
π− ⋅ = − ≈
8. The formula s r
θ= can only be used when
θ is
expressed in radians. Thus, we begin by converting
45° to radians. Multiply by radians
180
π
° .
radians 45
45 45 radians
180 180
radians
4
π
π
π
° = ° ⋅ =
°
=
Now we can use the formula s r
θ= to find the
length of the arc. The circle’s radius is 6 inches :
r = 6 inches. The measure of the central angle in
radians is :
4 4
π π
θ = . The length of the arc
intercepted by this central angle is
(6 inches) 4
6 inches
4
3 inches
2
4.71 inches.
s r
θ π
π
π
=
 
=  
 
=
=
≈
9. The formula 21
2
A r
θ= can only be used when
θ is
expressed in radians. Thus, we begin by converting
150° to radians. Multiply by radians
180
π
° .
radians
150 150 180
150 radians
180
5 radians
6
π
π
π
° = ° ⋅ °
=
=
The circle’s radius is 6 feet.
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2
5
(6 feet) 6
15 square feet
47.12 square feet
A r
θ
π
π
=
 
=  
 
=
≈
10. We are given
ω , the angular speed.
45
ω = revolutions per minute
We use the formula r
ν ω= to find ,v the linear
speed. Before applying the formula, we must express
ω in radians per minute.
45 revolutions 2 radians
1 minute 1 revolution
90 radians
1 minute
π
ω π
= ⋅
=
The angular speed of the propeller is 90
π radians per
minute. The linear speed is
90
1.5 inches 1 minute
135 inches
minute
inches
135 minute
inches
424 minute
r
ν ω π
π
π
=
= ⋅
=
=
≈
The linear speed is 135
π inches per minute, which is
approximately 424 inches per minute.

Section 1.1 Angles and Trigonometric Utilities
3
Concept and Vocabulary Check 1.1
1. origin; x-axis
2. counterclockwise; clockwise
3. acute; right; obtuse; straight
4. s
r
5. 180
π
°
6. 180
π
°
7. coterminal; 360° ; 2
π
8. r
θ
9. 21
2 r
θ
10. false
11. r
ω ; angular
Exercise Set 1.1
1. obtuse
2. obtuse
3. acute
4. acute
5. straight
6. right
7. 40 inches 4 radians
10 inches
s
r
θ = = =
8. 30 feet 6 radians
5 feet
s
r
θ = = =
9. 8 yards 4 radians
6 yards 3
s
r
θ = = =
10. 18 yards 2.25 radians
8 yards
s
r
θ = = =
11. 400 centimeters 4 radians
100 centimeters
s
r
θ = = =
12. 600 centimeters 6 radians
100 centimeters
s
r
θ = = =
13. radians
45 45 180
45 radians
180
radians
4
π
π
π
° = ° ⋅ °
=
=
14. radians
18 18 180
18 radians
180
radians
10
π
π
π
° = ° ⋅ °
=
=
15. radians
135 135 180
135 radians
180
3 radians
4
π
π
π
° = ° ⋅ °
=
=
16. radians
150 150 180
150 radians
180
5 radians
6
π
π
π
° = ° ⋅ °
=
=
17. radians
300 300 180
300 radians
180
5 radians
3
π
π
π
° = ° ⋅ °
=
=
18. radians
330 330 180
330 radians
180
11 radians
6
π
π
π
° = ° ⋅ °
=
=
19. radians
225 225 180
225 radians
180
5 radians
4
π
π
π
− ° = − ° ⋅ °
= −
= −

Loading page 6...

Chapter 1 Angles and the Trigonometric Functions
4
20. radians
270 270 180
270 radians
180
3 radians
2
π
π
π
− ° = − ° ⋅ °
= −
= −
21.
oradians 180
radians
2 2 radians
π
π π
= ⋅
o180
2
o90
=
=
22.
oradians 180
radians
9 9 radians
π
π π
= ⋅
o180 o20
9
= =
23.
o2 2 radians 180
radians
3 3 radians
π
π π
= ⋅
o2 180
3
o120
⋅
=
=
24.
0 o3 radians 180 3 180 o135
4 radians 4
π π
⋅
⋅ = =
25.
o7 7 radians 180
radians
6 6 radians
π
π π
= ⋅
o7 180
6
o210
⋅
=
=
26.
o o11 radians 180 11 180 o330
6 radians 6
π π
⋅
⋅ = =
27.
o180
3 radians 3 radians radians
π
π π
− = − ⋅
o3 180
o540
= − ⋅
= −
28.
o180 o o4 radians 4 180 720
radians
π π
− ⋅ = − ⋅ = −
29. radians
18 18 180
18 radians
180
0.31 radians
π
π
° = ° ⋅ °
=
≈
30. radians
76 76 180
76 radians
180
1.33 radians
π
π
° = ° ⋅ °
=
≈
31. radians
40 40 180
40 radians
180
0.70 radians
π
π
− ° = − ° ⋅ °
= −
≈ −
32. radians
50 50 180
50 radians
180
0.87 radians
π
π
− ° = − ° ⋅ °
= −
≈ −
33. radians
200 200 180
200 radians
180
3.49 radians
π
π
° = ° ⋅ °
=
≈
34. radians
250 250 180
250 radians
180
4.36 radians
π
π
° = ° ⋅ °
=
≈
35.
o180
2 radians 2 radians radians
π
= ⋅
o2 180
o114.59
π
⋅
=
≈
36.
o o180 3 180 o3 radians 171.89
radians
π
π
⋅
⋅ = ≈
37.
oradians 180
radians
13 13 radians
π
π π
= ⋅
o180
13 o13.85
=
≈

Loading page 7...

Loading page 8...

Chapter 1 Angles and the Trigonometric Functions
6
53.
54.
55.
56.
57. 395 360 35° − ° = °
58. 415 360 55° − ° = °
59. 150 360 210− ° + ° = °
60. 160 360 200− ° + ° = °
61. 765 360 3 765 1080 315− ° + ° ⋅ = − ° + ° = °
62. 760 360 3 760 1080 320− ° + ° ⋅ = − ° + ° = °
63. 19 19 12 7
2
6 6 6 6
π
π π π
π− = − =
64. 17 17 10 7
2
5 5 5 5
π
π π π
π− = − =
65. 23 23 23 20 3
2 2 4
5 5 5 5 5
π
π
π π π
π
π− ⋅ = − = − =
66. 25 25 25 24
2 2 4
6 6 6 6 6
π
π
π π π
π
π− ⋅ = − = − =
67. 100 99
2
50 50 50 50
π
π π π
π− + = − + =
68. 80 79
2
40 40 40 40
π
π π π
π− + = − + =
69. 31 31
2 3 6
7 7
π
π
π
π− + ⋅ = − +
31 42 11
7 7 7
π π π
= − + =
70. 38 38
2 3 6
9 9
π
π
π
π− + ⋅ = − + 38 54 16
9 9 9
π π π
= − + =
71. 12 inches, 45r
θ= = °
Begin by converting 45° to radians, in order to use
the formula s r
θ= .
radians
45 45 radians
180 4
π
π
° = °⋅ =
°
Now use the formula s r
θ= .
12 3 inches 9.42 inches
4
s r
π
θ
π= = ⋅ = ≈
72. 16 inches, 60r
θ= = °
Begin by converting 60° to radians, in order to use
the formula s r
θ= .
radians
60 60 radians
180 3
π
π
° = ° ⋅ =
°
Now use the formula s r
θ= .
16
16 inches 16.76 inches
3 3
s r
π π
θ= = ⋅ = ≈
73. 8 feet, 225r
θ= = °
Begin by converting 225° to radians, in order to use
the formula s r
θ= .
radians 5
225 225 radians
180 4
π
π
° = °⋅ =
°
Now use the formula s r
θ= .
5
8 10 feet 31.42 feet
4
s r
π
θ
π= = ⋅ = ≈
74. 9 yards, 315r
θ= = °
Begin by converting 315° to radians, in order to use
the formula s r
θ= .
radians 7
315 315 radians
180 4
π
π
° = ° ⋅ =
°
Now use the formula s r
θ= .
7 63
9 yards 49.48 yards
4 4
s r
π π
θ= = ⋅ = ≈

Loading page 9...

Section 1.1 Angles and Trigonometric Utilities
7
75. Begin by converting the angle to radians.
radians
18 18 radians
180 10
π
π
° = °⋅ =
°
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2 (10 meters) 10
5 square meters
15.71 square meters
A r
θ π
π
=
 
=  
 
=
≈
76. Begin by converting the angle to radians.
radians
15 15 180
radians
12
π
π
° = ° ⋅ °
=
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2 (6 yards) 12
3 square yards
2
4.71 square yards
A r
θ π
π
=
 
=  
 
=
≈
77. Begin by converting the angle to radians.
radians
240 240 180
4 radians
3
π
π
° = ° ⋅ °
=
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2
4
(4 inches) 3
32 square inches
3
33.51 square inches
A r
θ π
π
=
 
=  
 
=
≈
78. Begin by converting the angle to radians.
radians
330 330 180
11 radians
6
π
π
° = ° ⋅ °
=
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2
11
(3 inches) 6
33 square inches
4
25.92 square inches
A r
θ π
π
=
 
=  
 
=
≈
79. 6 revolutions per second
6 revolutions 2 radians 12 radians
1 second 1 revolutions 1 seconds
12 radians per second
π
π
π
= ⋅ =
=
80. 20 revolutions per second
20 revolutions 2 radians 40 radians
1 second 1 revolution 1 second
40 radians per second
π
π
π
= ⋅ =
=
81. 4 2
and
3 3
π π
−
82. 7 5
and
6 6
π π
−
83. 3 5
and
4 4
π π
−
84. 7
and
4 4
π π
−
85. 3
and
2 2
π π
−
86. −
π and
π
87. 55 11
2
60 6
π
π⋅ =
88. 35 7
2
60 6
π
π⋅ =

Loading page 10...

Chapter 1 Angles and the Trigonometric Functions
8
89. 3 minutes and 40 seconds equals 220 seconds.
220 22
2
60 3
π
π⋅ =
90. 4 minutes and 25 seconds equals 265 seconds.
265 53
2
60 6
π
π⋅ =
91. 21
2
A r
θ=
21
2
21
2
25 square feet (10 feet)
25 square feet
(10 feet)
25
50
1 radians
2
θ
θ
θ
θ
=
=
=
=
92. 21
2
21
2
21
2
36 square yards (6 yards)
36 square yards
(6 yards)
36
18
2 radians
A r
θ
θ
θ
θ
θ
=
=
=
=
=
93. First, convert to degrees.
1 1 360
revolution revolution
6 6 1 revolution
1 360 60
6
°
= ⋅
= ⋅ ° = °
Now, convert 60° to radians.
radians 60
60 60 radians
180 180
radians
3
π
π
π
° = ° ⋅ =
°
=
Therefore, 1
6 revolution is equivalent to 60° or 3
π
radians.
94. First, convert to degrees.
o1 1 360
revolutions revolutions
3 3 1 revolution
1 o o360 120
3
= ⋅
= ⋅ =
Now, convert 120° to radians.
radians 120 2
120 120 radians radians
180 180 3
π
π
π
° = ° ⋅ = =
°
Therefore, 1
3 revolution is equivalent to 120° or 2
3
π
radians.
95. The distance that the tip of the minute hand moves is
given by its arc length, s. Since s r
θ= , we begin by
finding r and
θ . We are given that r = 8 inches. The
minute hand moves from 12 to 2 o'clock, or 1
6 of a
complete revolution. The formula s r
θ= can only be
used when
θ is expressed in radians. We must
convert 1
6 revolution to radians.
1 1 2 radians
revolution revolution
6 6 1 revolution
radians
3
π
π
= ⋅
=
The distance the tip of the minute hand moves is
8
(8 inches) inches 8.38 inches.
3 3
s r
π π
θ  
= = = ≈ 
 
96. The distance that the tip of the minute hand moves is
given by its arc length, s. Since s r
θ= , we begin by
finding r and
θ . We are given that
r = 6 inches. The minute hand moves from 12 to 4
o’clock, or 1
3 of a complete revolution. The formula
s r
θ= can only be used when
θ is expressed in
radians. We must convert 1
3 revolution to radians.
1 1 2 radians
revolution revolution
3 3 1 revolution
2 radians
3
π
π
= ⋅
=
The distance the tip of the minute hand moves is
2 12
(6 inches) inches
3 3
4 inches 12.57 inches.
s r
π π
θ
π
 
= = = 
 
= ≈

Loading page 11...

Section 1.1 Angles and Trigonometric Utilities
9
97. The length of each arc is given by s r
θ= . We are
given that r = 24 inches and
90 .
θ = ° The formula s r
θ= can only be used when
θ is expressed in radians.
radians 90
90 90 radians
180 180
= radians
2
π
π
π
° = ° ⋅ =
°
The length of each arc is
(24 inches) 12 inches
2
37.70 inches.
s r
π
θ
π
 
= = = 
 
≈
98. The distance that the wheel moves is given by
s r
θ= . We are given that r = 80 centimeters and
θ
= 60°. The formula s r
θ= can only be used when
θ
is expressed in radians.
radians 60
60 60 radians
180 180
= radians
3
π
π
π
° = ° ⋅ =
°
The length that the wheel moves is
80
(80 centimeters) centimeters
3 3
83.78 centimeters.
s r
π π
θ  
= = = 
 
≈
99. Begin by converting the angle to radians.
radians
135 135 180
3 radians
4
π
π
° = ° ⋅ °
=
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2
3
(40 feet) 4
600 square feet
1884.96 square feet
A r
θ π
π
=
 
=  
 
=
≈
100. Begin by converting the angle to radians.
radians
120 120 180
2 radians
3
π
π
° = ° ⋅ °
=
Now use the formula 21
2
A r
θ= to find the area of
the sector.:
21
2
21
2
2
(30 feet) 3
300 square feet
942.48 square feet
A r
θ π
π
=
 
=  
 
=
≈
101. Recall that s
r
θ = . We are given that
s = 8000 miles and r = 4000 miles.
8000 miles 2 radians
4000 miles
s
r
θ = = =
Now, convert 2 radians to degrees.
o180 o2 radians 2 radians 114.59
radians
π
= ⋅ ≈
102. Recall that s
r
θ = . We are given that
s = 10,000 miles and r = 4000 miles.
10, 000 miles 2.5 radians
4000 miles
s
r
θ = = =
Now, convert 2.5 radians to degrees.
o180 o2.5 radians 143.24
2 radians
π
⋅ ≈
103. Recall that s r
θ= . We are given that
r = 4000 miles and 30
θ = ° . The formula s r
θ= can
only be used when
θ is expressed in radians.
radians 30
30 30 radians
180 180
radians
6
= =(4000 miles) 2094 miles
6
s r
π
π
π π
θ
° = ° ⋅ =
°
=
  ≈ 
 
To the nearest mile, the distance from A to B is
2094 miles.
104. Recall that s r
θ= . We are given that
r = 4000 miles and 10
θ = ° . We can only use the
formula s r
θ= when
θ is expressed in radians.
radians 10
10 10 radians
180 180
radians
18
= =(4000 miles) 698 miles
18
s r
π
π
π π
θ
° = ° ⋅ =
°
=
  ≈ 
 
To the nearest mile, the distance from A to B is
698 miles.

Loading page 12...

Chapter 1 Angles and the Trigonometric Functions
10
105. Linear speed is given by r
ν ω= . We are given that
12
π
ω = radians per hour and
r = 4000 miles. Therefore,
(4000 miles) 12
4000 miles per hour
12
1047 miles per hour
r
π
ν ω
π
 
= =  
 
=
≈
The linear speed is about 1047 miles per hour.
106. Linear speed is given by r
ν ω= . We are given that
r = 25 feet and the wheel rotates at 2 revolutions per
minute. We need to convert 2 revolutions per minute
to radians per minute.
2 revolutions per minute
2 radians
2 revolutions per minute 1 revolution
4 radians per minute
π
π
= ⋅
=
(25 feet)(4 ) 314 feet per minuter
ν ω
π= = ≈
The linear speed of the Ferris wheel is about
314 feet per minute.
107. Linear speed is given by r
ν ω= . We are given that r
= 12 feet and the wheel rotates at 20 revolutions per
minute.
20 revolutions per minute
2 radians
20 revolutions per minute 1 revolution
40 radians per minute
π
π
= ⋅
=
(12 feet)(40 )
1508 feet per minute
r
ν ω
π= =
≈
The linear speed of the wheel is about
1508 feet per minute.
108. Begin by converting 2.5 revolutions per minute to
radians per minute.
2.5 revolutions per minute
2 radians
2.5 revolutions per minute 1 revolution
5 radians per minute
π
π
= ⋅
=
The linear speed of the animals in the outer rows is
(20 feet)(5 ) 100 feet per minuter
ν ω
π= = ≈
The linear speed of the animals in the inner rows is
(10 feet)(5 ) 50 feet per minuter
ν ω
π= = ≈
The difference is 100 50 50
π π π− = feet per minute
or about 157 feet per minute.
109. – 120. Answers may vary.
121. 30 15'10 '' 30.25= 
122. 65 45'20 '' 65.76= 
123. 30.42 30 25'12 ''= 
124. 50.42 50 25'12 ''= 
125. does not make sense; Explanations will vary.
Sample explanation: Angles greater than
π will
exceed a straight angle.
126. does not make sense; Explanations will vary.
Sample explanation: It is possible for
π to be used
in an angle measured using degrees.
127. makes sense
128. does not make sense; Explanations will vary.
Sample explanation: That will not be possible if the
angle is a multiple of 2 .
π
129. A right angle measures 90° and
90 2
π
° = radians ≈ 1.57 radians.
If 3 radians 1.5 radians,
2
θ
θ= = is smaller than a
right angle.
130. s r
θ=
Begin by changing 20
θ = ° to radians.
20 20 radians
180 9
100= 9
900 286 miles
r
r
π π
π
π
° = ° ⋅ =
°
= ≈
To the nearest mile, a radius of 286 miles should be
used.
131. 21
2
A r
θ=
21
2
21
2
700 square feet (30 feet)
700 square feet
(30 feet)
700
450
14 radians
9
θ
θ
θ
θ
=
=
=
=
Covvert radians to degrees:
14 14 180
radians 89
9 9
π
°
= ⋅ ≈ °
The sprinkler should rotate about 89 .°

Loading page 13...

Section 1.2 Right Triangle Trigonometry
11
132. s r
θ=
Begin by changing 26
θ = ° to radians.
13
26 26 radians
180 90
13
=4000 90
1815 miles
s
π π
π
° = ° ⋅ =
°
⋅
≈
To the nearest mile, Miami, Florida is 1815 miles
north of the equator.
133. First find the hypotenuse.
2 2 2
2 2 2
2
2
5 12
25 144
169
13
c a b
c
c
cc
= +
= +
= +
=
=
Next write the ratio.
5
13
a
c =
134. First find the hypotenuse.
2 2 2
2 2 2
2
2
1 1
1 1
2
2
c a b
c
c
c
c
= +
= +
= +
=
=
Next write the ratio and simplify.
1
2
1 2
2 2
2
2
a
c =
= ⋅
=
135.
2 2 2 2
2 2
2 2
2
a b a b
c c c c
a b
c
   
+ = +   
   
+
=
Since 2 2 2 ,c a b= + continue simplifying by
substituting 2
c for 2 2 .a b+
Section 1.2
Check Point Exercises
1. Use the Pythagorean Theorem, 2 2 2
c a b= + , to find
c.
2 2 2 2 2
3, 4
3 4 9 16 25
25 5
a b
c a b
c
= =
= + = + = + =
= =
Referring to these lengths as opposite, adjacent, and
hypotenuse, we have
opposite 3
sin hypotenuse 5
adjacent 4
cos hypotenuse 5
opposite 3
tan adjacent 4
θ
θ
θ
= =
= =
= =
hypotenuse 5
csc opposite 3
hypotenuse 5
sec adjacent 4
adjacent 4
cot opposite 3
θ
θ
θ
= =
= =
= =
2. Use the Pythagorean Theorem, 2 2 2
c a b= + , to
find b.
2 2 2
2 2 2
2
2
1 5
1 25
24
24 2 6
a b c
b
b
b
b
+ =
+ =
+ =
=
= =
Note that side a is opposite
θ and side b is adjacent
to
θ .
opposite 1
sin hypotenuse 5
adjacent 2 6
cos hypotenuse 5
opposite 1 6
tan adjacent 122 6
hypotenuse 5
csc 5
opposite 1
hypotenuse 5 5 6
sec adjacent 122 6
adjacent 2 6
cot 2 6
opposite 1
θ
θ
θ
θ
θ
θ
= =
= =
= = =
= = =
= = =
= = =

Loading page 14...

Chapter 1 Angles and the Trigonometric Functions
12
3. Apply the definitions of these three trigonometric functions.
length of hypotenuse
csc 45 length of side opposite 45
2 2
1
length of hypotenuse
sec 45 length of side adjacent to 45
2 2
1
length of side adjacent to 45
cot 45 length of side opposite 45
1 1
1
° = °
= =
° = °
= =
°
° = °
= =
4. length of side opposite 60
tan 60 length of side adjacent to 60
3 3
1
length of side opposite 30
tan 30 length of side adjacent to 30
1 1 3 3
3 33 3
°
° = °
= =
°
° = °
= = ⋅ =
5.
2
sin 3tan cos 5
3
θ
θ θ
= =
2 3 2
3 5 5
2 5 2 5
55 5
= ⋅ =
= ⋅ =
1 1 3
csc 2sin 2
3
1 1 3
sec cos 5 5
3
3 5 3 5
55 5
1 1 5
cot 2tan 2
5
θ θ
θ θ
θ θ
= = =
= = =
= ⋅ =
= = =

Loading page 15...

Section 1.2 Right Triangle Trigonometry
13
6. We can find the value of cos
θ by using the Pythagorean identity.
2 2sin cos 1
2
1 2cos 1
2 1 2cos 1
4 12cos 1 4
32cos 4 3 3
cos 4 2
θ θ
θ
θ
θ
θ
θ
+ =
  + = 
 
+ =
= −
=
= =
7. a. o o o osin 46 cos(90 46 ) cos 44= − =
b. cot tan
12 2 12
6
tan 12 12
5
tan 12
π
π π
π π
π
 
= − 
 
 
= − 
 
=
8. Many Scientific Calculators
Function Mode Keystrokes Display
(rounded to four places)
a. sin 72.8° Degree 72.8 SIN 0.9553
b. csc 1.5 Radian 1.5 SIN 1/x 1.0025
Many Graphing Calculators
Function Mode Keystrokes Display
(rounded to four places)
a. sin 72.8° Degree SIN 72.8 ENTER 0.9553
b. csc 1.5 Radian ( SIN 1.5 ) x-1 ENTER 1.0025
9. Because we have a known angle, an unknown opposite side, and a known adjacent side, we select the
tangent function.
otan 24 750 o750 tan 24
750(0.4452) 333.9
a
a
a
=
=
≈ ≈
The distance across the lake is approximately 333.9 yards.

Loading page 16...

13 more pages available. Scroll down to load them.

Preview Mode

100%

Study Now!

XY-Copilot AI

Unlimited Access

Secure Payment

Instant Access

24/7 Support

Document Chat

Document Details

Subject

Mathematics

Solution Manual for Trigonometry, 2nd Edition

Study Now!

Document Details

Related Documents

Trigonometry, 2nd Edition Test Bank

AP Calculus AB Scoring Guide Unit 6 Progress Check

Clinical Psychologist

Module 4 Matrices

MATH 1324 Homework 5 Answers

Ap progress 1 5 all 5

The Fundamental Theorem of Calculus and Definite I

AP Calculus AB Scoring Guide

Investigating the Rising Cost of MTA Transit Fare

Module 11 Geometry

Company

Explore

Study Tools