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 265: 71

Answer

For the function $cot^{-1}~x$: The domain is $(-\infty, \infty)$ The range is $(0,\pi)$ We can see a sketch of the graph of $~~cot^{-1}~x~~$ below. Note there is a horizontal asymptote at $y = 0$ and $y = \pi$
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Work Step by Step

Consider the function $cot~x$: The domain is all real numbers except $~~\pi~n~~$, where $n$ is an integer The range is $(-\infty, \infty)$ We can consider the function $~~cot^{-1}~x~~$ as the inverse function of $~~cot~x~~$ by considering the domain of $~~cot~x~~$ restricted to $(0,\pi)$ Then for the function $cot^{-1}~x$: The domain is $(-\infty, \infty)$ The range is $(0,\pi)$ We can see a sketch of the graph of $~~cot^{-1}~x~~$ below. Note there is a horizontal asymptote at $y = 0$ and $y = \pi$
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