## Precalculus (6th Edition) Blitzer

The value of the expression is $-\frac{5\sqrt{11}}{11}$
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, $\cot \left[ {{\cos }^{-1}}\left( -\frac{5}{6} \right) \right]=\frac{-5\sqrt{11}}{11}$.