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: 10


$x=\frac{\pi}{2}+2n\pi$ $x=\frac{5\pi}{6}+2n\pi$ $x=\frac{7\pi}{6}+2n\pi$ where $n$ is an integer.

Work Step by Step

$cos~2x+sin~x=0$ $cos^2x-sin^2x+sin~x=0$ $1-sin^2x-sin^2x+sin~x=0$ $(1+sin~x)(1-sin~x)+sin~x(1-sin~x)=0$ $(1-sin~x)(1+2~sin~x)=0$ $sin~x=1$ and $sin~x=-\frac{1}{2}$ The solutions in $[0,2π)$ are: $x=\frac{\pi}{2}$ $x=\frac{5\pi}{6}$ $x=\frac{7\pi}{6}$ General solutions: $x=\frac{\pi}{2}+2n\pi$ $x=\frac{5\pi}{6}+2n\pi$ $x=\frac{7\pi}{6}+2n\pi$ where $n$ is an integer.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.