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: 45

Answer

$4k\pi+\frac{8\pi}{3}, 4k\pi+\frac{10\pi}{3}$. $\frac{8\pi}{3}, \frac{10\pi}{3}, \frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$

Work Step by Step

Using trigonometric identities, we have $sin(\frac{\theta}{2})=-\frac{\sqrt 3}{2} \longrightarrow \frac{\theta}{2}=2k\pi+\frac{4\pi}{3}, 2k\pi+\frac{5\pi}{3}, \longrightarrow \theta=4k\pi+\frac{8\pi}{3}, 4k\pi+\frac{10\pi}{3}$. Six examples $\theta=\frac{8\pi}{3}, \frac{10\pi}{3}, \frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$
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