Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.5 Inverse Circular Functions - 7.5 Exercises: 33

Answer

$y=0$

Work Step by Step

$y=\sec^{-1}x =$arcsec$x$ Domain: $(-\infty, -1]\cup[1, \infty)$ Range: $[0,\displaystyle \frac{\pi}{2})\cup(\frac{\pi}{2},\pi]$ Quadrants (unit circle): I and II -------- $y$ is the number from $[0,\displaystyle \frac{\pi}{2})\cup(\frac{\pi}{2},\pi]$ such that $\sec y=1$ $(\cos y=1)$ $\cos 0=1$, that is,$ \sec 0=1, $ and $0\displaystyle \in[0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi]$. So, $y=0$
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