Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 552: 27


$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.

Work Step by Step

$sin~x=\sqrt 3-sin~x$ $2~sin~x=\sqrt 3$ $sin~x=\frac{\sqrt 3}{2}$ The period of $sin~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are: $x=\frac{\pi}{3}$ and $x=\frac{2\pi}{3}$ Now, add multiples of $2\pi$ to each of the solutions: $x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.
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