Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.9: Area Problems
Problem 10P
Related questions
Concept explainers
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Topic Video
Question
43,49 plz
Transcribed Image Text:In Problems 35-42, sin 0 and cos 0 are given. Find the exact value of each of the four remaining trigonometric functions,
Trigônometric Functions
cos 1° + cos 2° + cos 3° + · · . + cos 358° + cos 359
97. For what numbers 0 is f(0) = tan 0 not defined?
99. For what numbers 0 is f(0) = sec 0 not defined?
98. For what numbers 0 is f(0) = cot 0 not defined?
100. For what numbers 0 is f(0) = csc 0 not defined?
35. sin 0 =
2V5
37. sin 0 =
4
1.
cos e =
5'
36. sin 0 =
5'
3
cos 0 = -
cos 0 =
Vs
1.
5
38. sin e
V5
2V5
cos 0 = -
V3
40. sin 0 =
V3
1.
cos e =
2
2. COS e =
5
39. sin 0 =
41. sin 0 =
3'
2V2
cos e =
2V2
3. cos 0 = -
1
42. sin 0 =
Ja
noltulo2
1.
In Problems 43–58, find the exact value of each of the remaining trigonometric functions of v.
12
43. sin 0 =
13'
5
to (1 45. cos 0 = -
5'
O in quadrant II
3
O in quadrant IV
5'
n quadrant III
44. cos e =
4
270° < 0 < 360°
5'
46. sin 0 =
13'
O in quadrant III
47. sin 0 =
5
90° < 0 < 180°
48. cos e =
13'
1
49, cos e = -
Inet (b) 51. sin e =
3'
2
tan 0 <0
<0 < T
50. sin 0 = -
3'
T < 0 <
3'
52. cos e = -
1
tan 0 > 0
4
53. sec 0 = 2,
sin 0 < 0
54. csc 0 = 3,
cot 0 <0
55. tan 0 =
sin 0 < 0
4'
4
cos e < 0
sin e >0
56. cot 0 =
57. tan 0 =
58. sec 0 = -2,
tan 0 > 0
snibneiz19bU tuoY 22922A
In Problems 59–76, use the even-odd properties to find the exact value of each expression. Do not use a calculator.
\ 59. sin (-60°)
60. cos (-30°)
62. sin (-135°)
61. tan (-30°)
63. sec(-60°)
64. csc(-30°)
65. sin (-90°)
66. cos (-270°)
67. tan -
68. sin (-7)
69. cos
70. sin -
ballea
71. tan (-7)
72. sin
37
73. csc
74. sec(-7)
YisludsboV hns zo
sec( -) io ol 76. cse(-
terbe no
In Problems 77–88, use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.
77. sin? 40° + cos? 40°
78. sec? 18° - tan? 18°
79. sin 80° csc 80°
80. tan 10° cot 10°
81. tan 40° -–
sin 40°
cos 20°
cos 40°
82. cot 20° -
83. cos 400° · sec 40°
sin 20°
84. tan 200° · cot 20°
25
37T
• cos
18
sin (-20°)
87.
cos 380°
85. sin
csc
12
86. sec
+ tan 200°
88.
cos (-430°)
sin 70°
+ tan (-70)
JOn o oiz s dons to suloy o
89. If sin 0 = 0.3, find the value of:
94. Find the exact value of:
sin 0 + sin (0 + 27) + sin (0 + 47)
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?
91. If tan 0 = 3, find the value of:
tan 0 + tan (0 + 7) + tan (0 + 27)
92. If cot 0 = -2, find the value of:
cot 0 + cot (0 - T) + cot (0 - 27)
101. What is the range of the sine function?
102. What is the range of the cosine function?
103. What is the range of the tangent function?
93. Find the exact value of:
sin 1° + sin 2° + sin 3° +... + sin 358° + sin 3599
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