Chapter 1 | Functions and Graphs
75
144. sin x (csc x −sin x ) 145. cos t sin t + sin t 1+cos t 146. 1+tan 2 α 1+cot 2 α For the following exercises, verify that each equation is an identity. 147. tan θ cot θ csc θ = sin θ 148. sec 2 θ tan θ = sec θ csc θ 149. sin t csc t + cos t sec t =1
163.
164.
sin x cos x +1 +
cos x −1 sin x
=0
150.
151. cot γ +tan γ = sec γ csc γ 152. sin 2 β +tan 2 β +cos 2 β = sec 2 β
1 1−sin α
=2sec 2 α
+ 1
153.
1+sin α
154. tan θ −cot θ sin θ cos θ
= sec 2 θ −csc 2 θ
For the following exercises, solve the trigonometric equations on the interval 0≤ θ <2 π . 155. 2sin θ −1=0
165.
156. 1+cos θ = 1 2 157. 2tan 2 θ =2 158. 4sin 2 θ −2=0
159. 3cot θ +1=0 160. 3sec θ −2 3=0 161. 2cos θ sin θ = sin θ 162. csc 2 θ +2csc θ +1=0
For the following exercises, each graph is of the form y = A sin Bx or y = A cos Bx , where B >0. Write the equation of the graph.
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