Calculus (3rd Edition)

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: 44


$$0, \frac{\pi}{3}, \pi, \frac{5 \pi}{3}$$

Work Step by Step

Since \begin{aligned} \sin \theta&=\sin 2 \theta\\ \sin \theta&=2 \sin \theta \cos \theta \\ \sin \theta-2 \sin \theta \cos \theta&=0\\ \sin \theta(1-2 \cos \theta)&=0 \end{aligned} Where we used the double angle identity $\sin 2 \theta=2 \sin \theta \cos \theta$ Then $$ \sin \theta=0 \text { or } 1-2 \cos \theta=0$$ Hence $$\theta \in\left\{0, \frac{\pi}{3}, \pi, \frac{5 \pi}{3}\right\}$$
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