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Chapter 1 | Functions and Graphs
1.3 EXERCISES For the following exercises, convert each angle in degrees to radians. Write the answer as a multiple of π . 113. 240° 114. 15° 115. −60° 116. −225° 117. 330° For the following exercises, convert each angle in radians to degrees. 118. π 2 rad 119. 7 π 6 rad 120. 11 π 2 rad 121. −3 π rad 122. 5 π 12 rad Evaluate the following functional values.
129. a =4, c =7 130. a =21, c =29 131. a =85.3, b =125.5
132. b =40, c =41 133. a =84, b =13 134. b =28, c =35
For the following exercises, P is a point on the unit circle. a. Find the (exact) missing coordinate value of each point and b. find the values of the six trigonometric functions for the angle θ with a terminal side that passes through point P . Rationalize denominators.
⎛ ⎝ 7
⎞ ⎠ , y >0
135. P
, y
25
⎛ ⎝ −15
y ⎞
⎛ ⎝ 4 π 3
⎞ ⎠
136. P
⎠ , y <0
123. cos
17 ,
⎛ ⎝ x , 7 3
⎞ ⎠ , x <0
124. tan ⎛
⎞ ⎠
⎝ 19 π 4
137. P
138. P ⎛
⎞ ⎠ , x >0
⎛ ⎝ − 3 π 4
⎞ ⎠
125. sin
⎝ x , − 15 4
126. sec ⎛
⎞ ⎠
⎝ π 6
For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. 139. tan 2 x +sin x csc x 140. sec x sin x cot x 141. tan 2 x sec 2 x 142. sec x −cos x 143. (1+tan θ ) 2 −2tan θ
⎛ ⎝ π
⎞ ⎠
127. sin
12
128. cos ⎛
⎞ ⎠
⎝ 5 π 12
For the following exercises, consider triangle ABC , a right triangle with a right angle at C. a. Find the missing side of the triangle. b. Find the six trigonometric function values for the angle at A . Where necessary, round to one decimal place.
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