Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - 7.3 Trigonometric Equations - 7.3 Assess Your Understanding - Page 466: 27

Answer

$\left\{\dfrac{\pi}{2}, \dfrac{7\pi}{6}, \dfrac{11\pi}{6}\right\}$

Work Step by Step

$\sin(3\theta)=-1$ $3\theta=\frac{3}{2}\pi+2k\pi$ $\theta=\frac{1}{2}\pi+\frac{2}{3}k\pi$ Those solutions where $0\le\theta\lt2\pi$ are only: $\theta=\frac{1}{2}\pi+\frac{2}{3}(0)\pi=\frac{1}{2}\pi$ $\theta=\frac{1}{2}\pi+\frac{2}{3}(1)\pi=\frac{7}{6}\pi$ $\theta=\frac{1}{2}\pi+\frac{2}{3}(2)\pi=\frac{11}{6}\pi$
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