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: 15


$x=\frac{\pi}{6}+2n\pi$, $x=\frac{5\pi}{6}+2n\pi$, $x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.

Work Step by Step

$3~sec^2x-4=0$ $3~sec^2x=4$ $sec^2x=\frac{4}{3}$ $sec~x=±\frac{2}{\sqrt 3}=±\frac{2}{\sqrt 3}\frac{\sqrt 3}{\sqrt 3}=±\frac{2\sqrt 3}{3}$ The period of $sec~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are: $x=\frac{\pi}{6}$, $x=\frac{5\pi}{6}$, $x=\frac{7\pi}{6}$ and $x=\frac{11\pi}{6}$ Now, add multiples of $2\pi$ to each of the solutions: $x=\frac{\pi}{6}+2n\pi$, $x=\frac{5\pi}{6}+2n\pi$, $x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.
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