In Problems 43–58, find the exact value of each of the remaining trigonometric funciions 12 43, sin e = O in quadrant II 13 O in quadrant IV 44. cos 0= < 180°
In Problems 43–58, find the exact value of each of the remaining trigonometric funciions 12 43, sin e = O in quadrant II 13 O in quadrant IV 44. cos 0= < 180°
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 59E
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Topic Video
Question
31,43
Transcribed Image Text:404 CHAPTER 6 Trigonometric Functions
2V5
5 d b 37. sin 0 =
V3
40. sin 0 =
35. sin 0 =
cos 0 = Vs
10
cos 0=
36. sin 0 =
cos 8=-
10
V3
V5
5. Cos 6 =-
2. Cos 0 = 1
2
2V5
cos e =
2
10
38. sin 0
39. sin e
2'
5
1.
2V2
cos 0 =
3
2V2
3. cos 6= -
3
noino2
41. sin 0=
42. sin 0=
In Problems 43–58, find the exact value of cach of the remaining trigonometric funciions o 0.
o 45. cos e =
0 in quadrant II
12
43. sin e =
O in quadrant II
O in quadrant IV
44. cos 0 =
270 < 0 < 36F
5'
5
48. cos 0 =
90° < 0 < 180°
13'
46. sin e = -
O in quadrant III
13"
47. sin 0 =
Imer () 51. sin o=
3'
2
tan 0 <0
1
49. cos e =
< 0 < T
3' 2
2
T < 0 <
50. sin e = -
2
3'
1
54. csc e = 3, cot 0 < 0
52. cos e = -
tan 0 > 0
4"
53. sec 0 = 2,
sin 0 < 0
3
sin 0 < 0
4
57. tan 0 =
3'
sin 0 >0
55. tan 0 =
56. cot 0 =
cos e < 0
woll
58. sec 0 = -2,
tan 0 > 0
gnibneizbU uoY 2292
In Problems 59–76, use the even-odd properties to find the exact value of each expression. Do not use a calculator.
62. sin (-135°)
59. sin (-60°)
60. cos (- 30°)
Trigonom
61. tan (-30°)
63. sec (-60°)
64. csc (- 30°)
65. sin (-90°) H
66. cos (-270°)
67. tan
68. sin (-7)
69. cos
70. sin
71. tan (-7)
72. sin
73. csc
74. sec(-T)
75. sec
76. csc
noirandt ineose bs oo
In Problems 77–88, use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.
78. sec? 18° - tan? 18° L 79. sin 80° csc 80°
77. sin? 40° + cos 40°
80. tan 10° cot 10°
sin 40°
cos 20°
81. tan 40° –
82. cot 20°
83. cos 400° • sec 40°()
84. tan 200° · cot 20°
cos 40°
sin 20°
het
sin (-20°)
87.
cos 380°
85. sin
25m
37
sin 70°
86. sec
csc
12
•cos
18
+ tan 200°
88.
cos (-430°)
+ tan(-70)
89. If sin 0 = 0.3, find the value of:
94. Find the exact value of:
OVE n
sin 0 + sin (0 + 27) + sin (0 + 47)
cos 1° + cos 2° + cos 3° +... + cos 358° + cos 359
90. If cos 0 = 0.2, find the value of:
95. What is the domain of the sine function?
cos 0 + cos (0 + 27) + cos (0 + 47)
96. What is the domain of the cosine function?
97. For what numbers 0 is f(e) = tan 0 not defined?
98. For what numbers 0 is f(0) = cot 0 not defined?
99. For what numbers 0 is f(0)
91. If tan 0 = 3, find the value of:
tan 0 + tan (0 + T) + tan(0 + 27)
92. If cot 0 = -2, find the value of:
= sec 0 not defined?
100. For what numbers 0 is f(0) = csc 0 not defined?
101. What is the range of the sine function?
cot 0 + cot (0 – T) + cot (0 - 27)
93. Find the exact value of:
102. What is the range of the cosine function?
sin 1° + sin 2° + sin 3° + · · .
+ sin 358° + sin 359°
103. What is the range of the tangent function?
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