Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.6 Trigonometric Equations - 7.6 Exercises - Page 720: 24


$\frac{\pi}{6}$, $\frac{\pi}{2}$, $\frac{3\pi}{2}$, $\frac{11\pi}{6}$

Work Step by Step

$2\cos^2 x-\sqrt{3}\cos x=0$ $\cos x(2\cos x-\sqrt{3})=0$ $\cos x=0$ or $2\cos x-\sqrt{3}=0$ If $\cos x=0$, the only solutions in $[0, 2\pi)$ are $\frac{\pi}{2}$ and $\frac{3\pi}{2}$. If $2\cos x-\sqrt{3}=0$: $2\cos x=\sqrt{3}$ $\cos x=\frac{\sqrt{3}}{2}$ The only solutions in $[0, 2\pi)$ are $\frac{\pi}{6}$ and $\frac{11\pi}{6}$.
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