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: 10

Answer

a. Domain:$ (-\infty, -1]\cup[1, \infty)$ Range:$[-\displaystyle \frac{\pi}{2},0)\cup(0,\frac{\pi}{2}]$ b. Domain:$ (-\infty, \infty) $ Range:$ (0, \pi)$ c. Domain:$ (-\infty, -1]\cup[1, \infty)$ Range:$ [0,\displaystyle \frac{\pi}{2})\cup(\frac{\pi}{2}\pi]$

Work Step by Step

See the table on page 703. a. $y=\csc^{-1}x$ Domain:$ (-\infty, -1]\cup[1, \infty)$ Range:$[-\displaystyle \frac{\pi}{2},0)\cup(0,\frac{\pi}{2}]$ b. $y=\cot^{-1}x$ Domain:$ (-\infty, \infty) $ Range:$ (0, \pi)$ c. $y=\sec^{-1}x$ Domain:$ (-\infty, -1]\cup[1, \infty)$ Range:$ [0,\displaystyle \frac{\pi}{2})\cup(\frac{\pi}{2}\pi]$
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