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: 11


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

Work Step by Step

$\sqrt 3~csc~x-2=0$ $\sqrt 3~csc~x=2$ $csc~x=\frac{2}{\sqrt 3}$ $csc~x=\frac{2}{\sqrt 3}·\frac{\sqrt 3}{\sqrt 3}=\frac{2\sqrt 3}{3}$ The period of $csc~x$ 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 $x=\frac{2\pi}{3}+2n\pi$
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