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 - Page 708: 26


$\arcsin(-\sqrt{2})$ does not exist

Work Step by Step

$y=\sin^{-1}x =\arcsin x$ Domain: $[-1, 1] $ Range: $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ ----------- $y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\sin y=-\sqrt{2}.$ Such a y can not exist, as $-1 \leq \sin y \leq 1$ ($-\sqrt{2}$ is not in the range of $\sin x,$ $-\sqrt{2}$ is not in the domain of $\sin^{-1}x$) so $\arcsin(-\sqrt{2})$ does not exist
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