548 CHAPTER 5 Trigonometric Functions Identify the quadrant (or possible quadrants) of an angle u that satisfies the given conditions. See Example 7. 109. sin u 70, csc u 70 110. cos u 70, sec u 70 111. cos u 70, sin u 70 112. sin u 70, tan u 70 113. tan u 60, cos u 60 114. cos u 60, sin u 60 115. sec u 70, csc u 70 116. csc u 70, cot u 70 117. sec u 60, csc u 60 118. cot u 60, sec u 60 119. sin u 60, csc u 60 120. tan u 60, cot u 60 Determine whether each statement is possible or impossible. See Example 8. 121. sin u = 2 122. sin u = 3 123. cos u = -0.96 124. cos u = -0.56 125. tan u = 0.93 126. cot u = 0.93 127. sec u = -0.3 128. sec u = -0.9 129. csc u = 100 130. csc u = -100 Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 9–11. 131. Find cos u, given that sin u = 3 5 and u is in quadrant II. 132. Find sin u, given that cos u = 4 5 and u is in quadrant IV. 133. Find csc u, given that cot u = - 1 2 and u is in quadrant IV. 134. Find sec u, given that tan u = 27 3 and u is in quadrant III. 135. Find tan u, given that sin u = 1 2 and u is in quadrant II. 136. Find cot u, given that csc u = -2 and u is in quadrant III. 137. Find cot u, given that csc u = -1.45 and u is in quadrant III. 138. Find tan u, given that sin u = 0.6 and u is in quadrant II. Give all six trigonometric function values for each angle u. Rationalize denominators when applicable. See Examples 9–11. 139. tan u = - 15 8 , and u is in quadrant II 140. cos u = - 3 5, and u is in quadrant III 141. sin u = 25 7 , and u is in quadrant I 142. tan u = 23, and u is in quadrant III 143. cot u = 23 8 , and u is in quadrant I 144. csc u = 2, and u is in quadrant II 145. sin u = 22 6 , and cos u 60 146. cos u = 25 8 , and tan u 60 147. sec u = -4, and sin u 70 148. csc u = -3, and cos u 70 149. sin u = 1 150. cos u = 1 Work each problem. 151. Derive the identity 1 + cot2 u = csc2 u by dividing x2 + y2 = r2 by y2. 152. Derive the quotient identity cos u sin u = cot u. Concept Check Suppose that 90° 6u 6180°. Find the sign of each function value. 153. sin 2u 154. csc 2u 155. tan u 2 156. cot u 2 Concept Check Suppose that -90° 6u 690°. Find the sign of each function value. 157. cos u 2 158. sec u 2 159. sec1-u2 160. cos1-u2
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