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: 8

Answer

a. $[-1, 1] $ b. $[0, \pi]$ c. decreasing d. because $-\displaystyle \frac{4\pi}{3}\not\in[0, \pi]$

Work Step by Step

See figure 17 on p.701 (or the table on page 703 ) In order to have an inverse, the domain of $\cos x$ is restricted to $[0, \pi]$. $y=\cos^{-1}x$ ($y$ is the number from $[0, \pi]$ for which $\cos y=x$) Domain:$[-1, 1] $ Range:$ [0, \pi]$ Quadrants (unit circle): I and II Figure 17: $\cos^{-1}x$ is decreasing. For part (d), $y=\displaystyle \frac{2\pi}{3}$ is the number from $[0, \pi]$ for which $\displaystyle \cos y=-\frac{1}{2}$ $-\displaystyle \frac{4\pi}{3}\not\in[0, \pi]$ (not in the range)
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