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 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 280: 24

Answer

The right side of the equation $\sin^{-1}{x} = \cos^{-1}{(-2)}$ is undefined so the equation does not have a solution. This is because in $\cos^{-1}{(x)}$, $x$ can only be a number from $-1$ to $1$.

Work Step by Step

RECALL: The value of $x$ in $\cos^{-1}{x}$ can only be a real number in the interval $[-1, 1]$. Thus, the right side of the equation $\sin^{-1}{x} = \cos^{-1}{(-2)}$ is undefined so the equation does not have a solution.
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