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: 25


$\frac{7\pi}{6}$, $\frac{3\pi}{2}$, $\frac{11\pi}{6}$

Work Step by Step

$-2\sin^2x=3\sin x+1$ $2\sin^2x+3\sin x+1=0$ $(2\sin x+1)(\sin x+1)=0$ $2\sin x+1=0$ or $\sin x+1=0$ If $2\sin x+1=0$: $2\sin x=-1$ $\sin x=-\frac{1}{2}$ The only solutions in $[0, 2\pi)$ are $\frac{7\pi}{6}$ and $\frac{11\pi}{6}$. If $\sin x+1=0$: $\sin x=-1$ The only solution in $[0, 2\pi)$ is $\frac{3\pi}{2}$.
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