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: 30


$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.

Work Step by Step

$\frac{1}{2}sec~x-1=0$ $\frac{1}{2}sec~x=1$ $sec~x=2$ The period of $sec~x$ is $2\pi$. The solutions in the interval: $[0,2π)$ are: $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$ Now, add multiples of $2\pi$ to each of the solutions: $x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.
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