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: 48


$\cos^{-1}(-2)$ does not exist.

Work Step by Step

Solve for radians, then convert to degrees. $y=\cos^{-1}x$ Domain:$[-1, 1] $ Range: $[0, \pi]$ Quadrants (unit circle): I and II -------- $y$ is the number from $[0, \pi]$ such that $\cos y=-2.$ But, such a y does not exist, as cosine can not be less than $-1$. More directly, $-2$ is not in the domain of $\cos^{-1}x$, so $\cos^{-1}(-2)$ does not exist.
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