Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.2 - More on Trigonometric Equations - 6.2 Problem Set - Page 332: 11



Work Step by Step

$sec(\theta)-2tan(\theta)=0$ $\frac{1}{cos(\theta)}-2\frac{sin(\theta)}{cos(\theta)}=0\;\;\;\;\;\;\;\;\;\;$ multiply each side by $cos(\theta)$. $1-2sin(\theta)=0$ $-2sin(\Theta )=-1\;\;\;\;\;\;\;\;\;\;$ subtract $ 1 $ from each side. $sin(\Theta )=\frac{-1}{-2} \;\;\;\;\;\;\;\;\;\;\;$ divide each side by $ -2 $ $sin(\Theta )=\frac{1}{2}$ $\theta= sin^{-1}(\frac{1}{2})$ We know $ sin(\theta) $ is positive in quadrant $I$ and quadrant $II$ $\theta=30^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=180^o-30^o=150^o$ $\theta=30^o\;\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\theta=150^o$ $\theta=\{30^o,150^o\}$
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