Answer
$$\sin (\theta+\pi) =-\sin \theta$$
Work Step by Step
Since
\begin{aligned}
\sin (\theta+\pi) &=\sin \theta \cos \pi+\cos \theta \sin \pi \\
&=\sin \theta(-1)+\cos \theta(0) \\
\end{aligned}
Then $$\sin (\theta+\pi) =-\sin \theta$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 1 - Precalculus Review - 1.4 Trigonometric Functions - Exercises - Page 31: 50
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