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 340: 14

Answer

$x=\{\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}\}$

Work Step by Step

$csc(3x)=1$ $\frac{1}{sin(3x)}=1$ $sin(3x)=1$ $3x=sin^{-1}(1)$ We know $sin(x)$ is positive in quardent $I$ and quardent $II$ The period of the sine function is $2\pi$ $3x=\frac{\pi}{2}\;\;\;\;or\;\;\;\;\;\;3x=2\pi+ \frac{\pi}{2}\;\;\;\;or\;\;\;\;\;\;3x=4\pi + \frac{\pi}{2}\;\;\;\;\;\;\;\;\;\; $ $x=\frac{\pi}{6}\;\;\;\;or\;\;\;\;\;\;x=\frac{5\pi}{6}\;\;\;\;or\;\;\;\;\;\;x=\frac{3\pi}{2}\;\;\;\;\;\;\;\;\;\;\;\;\;$ $x=\{\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}\}$
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