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 333: 44

Answer

$\theta=150^o+360k\;\;\;\;\;\;\;\;\;\;\;\;\;,\;\;\;\;\;\;\;\;\theta=210^o+360k$

Work Step by Step

$2\sqrt{3}sec(\theta)+7=3$ $\frac{2\sqrt{3}}{cos(\theta)}=3-7$ $2\sqrt{3}=-4cos(\theta)$ $cos(\theta)=\frac{-\sqrt{3}}{2}$ $\theta=cos^{-1}(\frac{-\sqrt{3}}{2})$ We know $cos(\theta)$ is negative in quadrant $II$ and $III$ $\theta=180^o-30^o=150^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=180^o+30^o=210^o$ $\theta=150^o+360k\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=210^o+360k\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;where \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;k=\{0,1,2,3,......\}$ $\theta=150^o+360k\;\;\;\;\;\;\;\;\;\;\;\;\;,\;\;\;\;\;\;\;\;\theta=210^o+360k$
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