University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.9 - Inverse Trigonometric Functions - Exercises - Page 181: 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 (if in doubt), 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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