Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 548: 7


$x=n\pi$, $x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$

Work Step by Step

$sin~2x-sin~x=0$ $2~sin~x~cos~x-sin~x=0$ $sin~x~(2~cos~x-1)=0$ $sin~x=0$ or $cos~x=\frac{1}{2}$ The solutions in $[0,2\pi)$ are: $x=0$, $x=\frac{\pi}{3}$, $x=\pi$ and $x=\frac{5\pi}{3}$ General solution: $x=2n\pi$, $x=\frac{\pi}{3}+2n\pi$, $x=\pi+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$ or $x=n\pi$, $x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$
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