Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - Chapter Review - Cumulative Review - Page 701: 7


$\theta=\dfrac{\pi}{12}+n\pi$ and $\theta=\dfrac{5\pi}{12}+n\pi$

Work Step by Step

We are given the equation: $\sin (2\theta)=0.5$ $\sin (2\theta)=\dfrac{1}{2}$ The angles $2\theta$ in $[0,2\pi)$ matching the equation are: $2\theta=\dfrac{\pi}{6}$ and $2\theta=\dfrac{5\pi}{6}$ Given the fact that the function has a period of $2\pi$, the solutions are: $2\theta=\dfrac{\pi}{6}+2n\pi$ and $2\theta=\dfrac{5\pi}{6}+2n\pi$ We determine $\theta$: $\theta=\dfrac{\pi}{12}+n\pi$ and $\theta=\dfrac{5\pi}{12}+n\pi$
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