Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Cumulative Review Exercises - Page 1128: 50


The value of the expression is $-\frac{5\sqrt{11}}{11}$

Work Step by Step

We have the provided expression as $\cot \left[ {{\cos }^{-1}}\left( -\frac{5}{6} \right) \right]$. Let us assume $\begin{align} & \left[ {{\cos }^{-1}}\left( -\frac{5}{6} \right) \right]=\theta \\ & \cos \theta =\frac{-5}{6} \end{align}$ Then, $\theta $ lies in the 2nd quadrant. And the expression reduces to $\cot \theta $ $\cot \theta =\frac{\cos \theta }{\begin{align} & \sqrt{1-{{\cos }^{2}}\theta } \\ & =\frac{\frac{-5}{6}}{\sqrt{1-\frac{25}{36}}} \\ & =\frac{-5\sqrt{11}}{11} \\ \end{align}}$ Hence, $\cot \left[ {{\cos }^{-1}}\left( -\frac{5}{6} \right) \right]=\frac{-5\sqrt{11}}{11}$.
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