Trigonometry 7th Edition

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

Chapter 6 - Section 6.3 - Trigonometric Equations Involving Multiple Angles - 6.3 Problem Set - Page 339: 6



Work Step by Step

$sin(2\theta)=\frac{\sqrt{-3}}{2}$ $2\theta=sin^{-1}(\frac{\sqrt{-3}}{2})$ We know $sin(\theta)$ is negative in quardent $III$ and quardent $IV$ The period of the sine function is $360^o$ $2\theta=180^o+60^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o+240^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o-60^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o+300^o$ $\theta=120^o\;\;\;\;or\;\;\;\;\;\;\theta=300^o\;\;\;\;or\;\;\;\;\;\;\theta=150^o\;\;\;\;or\;\;\;\;\;\;\theta=330\;\;\;$ $\theta=\{120^o,150^o,300^o,330^o\}$
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