Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.3 - Solving Trigonometric Equations - 7.3 Exercises - Page 530: 19


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

Work Step by Step

$sin~x(sin~x+1)=0$ $sin~x=0$ or $sin~x=-1$ The period of $sin~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are: $x=0$, $x=\pi$, $x=\frac{3\pi}{2}$ Now, add multiples of $2\pi$ to each of the solutions: $x=0+2n\pi=2n\pi$ $x=\pi+2n\pi$ $x=\frac{3\pi}{2}+2n\pi$ We can rewrite the solutions $x=2n\pi$ and $x=\pi+2n\pi$ as: $x=n\pi$ Finally: $x=n\pi$ or $x=\frac{3\pi}{2}+2n\pi$, where $n$ is an integer.
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