Trigonometry (11th Edition) Clone

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

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 264: 26


$\sin^{-1}(-\sqrt{2})$ is not defined.

Work Step by Step

Inverse Sine Function $y=\sin^{-1}x$ or $y=$ arcsin $x$ means that $x=\sin y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$. ------------------- Since $-\sqrt{2} < 1$, there is no y such that $ \sin y=\sqrt{-2}$ $y=\sin^{-1}(-\sqrt{2})$ is not defined. $\sin^{-1}$or arcsin is the inverse of $\sin,$ so its domain must be the range of sine. The range of sine is $[-1,1]$ and $-\sqrt{2}\not\in [-1,1] )$
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