Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Review Exercises - Page 94: 44


We calculate $\cos^{-1}(0.1)$ or $\displaystyle \cos^{-1}(\frac{1}{10})$

Work Step by Step

$\sec^{-1}10$ is the angle $\theta$ for which $\sec\theta=10$ But sec and cos are reciprocal , $\displaystyle \sec\theta=\frac{1}{\cos\theta}$ so, if $\sec\theta=10$, then $\displaystyle \quad \cos\theta=\frac{1}{\sec\theta}=\frac{1}{10}=0.1$ So, $\theta$ is the angle for which the secant is 10, and the cosine is $0.1$. On our calculator, we have the $\cos^{-1}$ button. We find $\theta=\sec^{-1}10$ by calculating $\cos^{-1}(0.1)$ or $\displaystyle \cos^{-1}(\frac{1}{10})$
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