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 721: 35


$\{0^{o}, 30^{o}, 150^{o},180^{o}\}$

Work Step by Step

Factor out $\tan^{2}\theta$ on the LHS $\tan^{2}\theta (2\sin\theta-1)=0$ ... zero factor principle ... 1. $\quad\tan^{2}\theta=0$ or 2.$\quad 2\sin\theta-1=0$ 1. $\quad\tan^{2}\theta=0$ $\tan\theta=0\Rightarrow \theta=0^{o}, 180^{o}$ 2.$\quad 2\sin\theta-1=0\qquad/+1$ $2\sin\theta=1\qquad/\div 2$ $\displaystyle \sin\theta=\frac{1}{2}\qquad$ ... use the unit circle... $\theta=30^{o}, 150^{o}$ Solution set = $\{0^{o}, 30^{o}, 150^{o},180^{o}\}$
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