Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 56

$-0.31$

Note that $\cot {x}=\frac{1}{\tan{(x)}}$. Hence, $\cot^{-1}{x}=\tan^{-1} {\left(\frac{1}{x}\right)}$. Use a calculator in radian mode and round the result to decimal places to obtain $\cot^{-1}{(-\sqrt{10})}=\tan^{-1} {\left(\dfrac{1}{-\sqrt{10}}\right)}\approx-0.31$