Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.6 - Inverse Trigonometric Functions - Exercises 7.6 - Page 420: 14

Answer

$\pi$

Work Step by Step

$y=\cos^{-1}x$ is the number in $[0, \pi]$ for which $\cos y=x.$ As the value of cosine approaches $-1,$ (from the right, because it can't approach it from the left - cosine is never less than -1) the angle we approach (in radians) is $\pi$. Alternatively, we can reach the same conclusion by observing the graph of $y=\cos^{-1}x$ (also written as $\arccos x$) in the vicinity of x=-1. See below.
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