Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 258: 11

Answer

$\displaystyle \cos^{-1}(\frac{1}{a})$

Work Step by Step

Inverse of Secant: $y=\sec^{-1}x$ or $y=$ arcsec $x$ means that $x=\sec y$, for $0\leq y\leq\pi, y\displaystyle \neq\frac{\pi}{2}$. so $y=\sec^{-1}a$ means that $a=\sec y,$ ... $\sec y$ and $\cos y$ are reciprocal ... $ a=\displaystyle \frac{1}{\cos y}\qquad /\displaystyle \times\frac{\cos y}{a}$ $\displaystyle \cos y=\frac{1}{a}$ By definition of lnverse Cosine Function $y=\cos^{-1}x$ or $y=$ arccos $x$ means that $x=\cos y$, for $ 0\leq y\leq\pi$, so $\displaystyle \cos y=\frac{1}{a}$ means that $y=\displaystyle \cos^{-1}(\frac{1}{a})$ Calculating $y=\sec^{-1}a$, we calculate $\displaystyle \cos^{-1}(\frac{1}{a})$
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