Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - Chapter Review - Review Exercises - Page 507: 68

Answer

$\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

Work Step by Step

Step 1. $sec^2(\theta)=4 \longrightarrow sec\theta=\pm2 \longrightarrow cos\theta=\pm\frac{1}{2}$ Step 2. For $cos\theta=\frac{1}{2}$, we have $\theta=2k\pi+\frac{\pi}{3}$ and $\theta=2k\pi+\frac{5\pi}{3}$ Step 3. For $cos\theta=-\frac{1}{2}$, we have $\theta=2k\pi+\frac{2\pi}{3}$ and $\theta=2k\pi+\frac{4\pi}{3}$ Step 4. Within $[0,2\pi)$, we have $\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$
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