goometric Functions In Problems 35-42, sin e and cos are given. Find the exact value of each of the four remaining trigonometric functions 2V5 5 Cos 0- Vs 35. sin e=- 37. sin e= cos e 36. sin cos e - V5 38. sin e - 2V5 cos e - 40. sin e 39. sin e cos 2. Cos 2V2 41. sin e- - 2V cos e 3" 42. sin e cos - noltulo2 3 In Problems 43-58, find the exact value of each of the remaining trigonometric furnctions of o. 12 e in quadrant II 43. sin e O in quadrant IV 5' 45. cos e=- e in quadran 13' 44. cos e 4 46. sin e-- 13 e in quadrant I 5 90 0 53. sec e- 2, sin e<0 54. csc e = 3, cot e<0 4" 55. tan e 4' sin e <0 56. cot e = 4 cos e <0 3' 57. tan e = - sin e>0 58. sec e= -2, tan e>0 gnibnstziabnu uoY 22 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) 61. tan (-30) 62. sin (-135) 63. sec(-60) 64. csc (-30) 65. sin (-90) 66. cos (-270) 67. tan 68. sin(-) 69. cos 70. sin- 71. tan (-) 72. sin 73. cse- 74. sec(-) br 78. se( -) 76. csc 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 sin 40 80. tan 10° cot 10 cos 20 81. tan 40 - 82. cot 20- sin 20 cos 40 83. cos 400 sec 40 84. tan 200 - cot 20 25 37 sin (-20) 87. cos 380 85. sin csc 12 86. sec - 18 *cos 18 + tan 200 88. cos (-430) sin 70 + tan(-) 89. If sin 8- 0.3, find the value of: 94. Find the exact value of: sin e + sin (e + 2w) + sin (e + 4m) cos 1 + cos 2 + cos 3 + 90. If cos e = 0.2, find the value of: + cos 358 + cos 3 95. What is the domain of the sine function? 96. What is the domain of the cosine function? cos e + cos (0+ 2m) + cos (@ + 4m) 97. For what numbers e is f(e) - tan e not defined? 98. For what numbers 8 is f(0) - cot 8 not defined? 99. For what numbers e is f(0) = sec e not defined? 100. For what numbers 6 is f(0) 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? 91. If tan o- 3, find the value of: tan e + tan (0 + ) + tan (0 + 2m) 92. If cot e= -2, find the value of: cot e + cot (0- ) + cot (0- 2m) - ese e not defined? 93. Find the exact value of: sin 1 + sin 2 + sin 3 + + sin 358 + sin 35oe
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
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Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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