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: 11


$x=n\pi$ $x=\frac{\pi}{2}+n\pi$ where $n$ is an integer.

Work Step by Step

$sin~4x=sin~2(2x)=2~sin~2x~cos~2x$ $sin~4x=-2~sin~2x$ $2~sin~2x~cos~2x+2~sin~2x=0$ $2~sin~2x(cos~2x+1)=0$ $sin~2x=0$ or $cos~2x=-1$ $sin~2x=0$ $2x=0$ $x=0$ and $2x=\pi$ $x=\frac{\pi}{2}$ $cos~2x=-1$ $2x=\pi$ $x=\frac{\pi}{2}$ The period of both $sin~2x$ and $cos~2x$ is $\pi$. The general solutions are: $x=0+n\pi=n\pi$ $x=\frac{\pi}{2}+n\pi$ where $n$ is an integer.
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