533 5.1 Angles Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 77. 32° 78. 86° 79. 26° 30′ 80. 58° 40′ 81. -40° 82. -98° 83. -125° 30′ 84. -203° 20′ 85. 361° 86. 541° 87. -361° 88. -541° 89. 539° 90. 699° 91. 850° 92. 1000° 93. 5280° 94. 8440° 95. -5280° 96. -8440° Give two positive and two negative angles that are coterminal with the given quadrantal angle. 97. 90° 98. 180° 99. 0° 100. 270° Write an expression that generates all angles coterminal with each angle. Let n represent any integer. 101. 30° 102. 45° 103. 135° 104. 225° 105. -90° 106. -180° 107. 0° 108. 360° 109. Why do the answers to Exercises 107 and 108 give the same set of angles? 110. Concept Check Which two of the following are not coterminal with r°? A. 360° + r° B. r° - 360° C. 360° - r° D. r° + 180° Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 111. 75° 112. 89° 113. 174° 114. 234° 115. 300° 116. 512° 117. -61° 118. -159° 119. 90° 120. 180° 121. -90° 122. -180° Solve each problem. See Example 6. 123. Revolutions of a Turntable A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second? 124. Revolutions of a Windmill A windmill makes 90 revolutions per min. How many revolutions does it make per second? 125. Rotating Tire A tire is rotating 600 times per min. Through how many degrees does a point on the edge of the tire move in 1 2 sec? 126. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec. 127. Rotating Pulley A pulley rotates through 75° in 1 min. How many rotations does the pulley make in 1 hr?
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