Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.4 - Introduction to Identities - 1.4 Problem Set - Page 40: 44


$\sec\theta$ = - $\frac{25}{24}$

Work Step by Step

We know from third Pythagorean identity that- $\sec\theta$ = ± $\sqrt (1+\tan^{2}\theta)$ As $\cos\theta\lt0$, i.e. $\cos\theta$ is negative and $\tan\theta$ is positive, hence $\theta$ terminates in Q III, Therefore $\sec\theta$ will be negative- $\sec\theta$ = - $\sqrt (1+\tan^{2}\theta)$ substitute the given value of $\tan\theta$- $\sec\theta$ = - $\sqrt (1+(\frac{7}{24})^{2})$ $\sec\theta$= - $\sqrt (1+\frac{49}{576})$ $\sec\theta$ = - $\sqrt (\frac{576+49}{576})$ = $\sqrt (\frac{625}{576})$ $\sec\theta$ = - $\frac{25}{24}$
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