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: 34

Answer

$\frac{4\pi}{27},\frac{22\pi}{27},\frac{40\pi}{27}$

Work Step by Step

Using trigonometric identities, we have $sin(3\theta+\frac{\pi}{18})=1 \longrightarrow 3\theta+\frac{\pi}{18}=\frac{\pi}{2}, \frac{5\pi}{2}, \frac{9\pi}{2} \longrightarrow \theta=\frac{4\pi}{27},\frac{22\pi}{27},\frac{40\pi}{27}$
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