# When working in decimal radians, how do you find the cot^-1(-5)?

Use your calculator and compute it as ${\cot}^{- 1} \left(- 5\right) = {\tan}^{- 1} \left(- \frac{1}{5}\right) \approx - 0.197396$ radians.
Since $\cot \left(\theta\right) = \frac{1}{\tan} \left(\theta\right)$, it follows that ${\cot}^{- 1} \left(5\right)$ can be thought of as an angle $\theta$ in a right triangle where the ratio of the adjacent side over the opposite side is $5 = \frac{5}{1}$. Therefore, the tangent of that angle $\theta$ is $\frac{1}{5}$ (opposite over adjacent).
Now the tangent function is an odd function, so $\tan \left(- \theta\right) = - \frac{1}{5}$ and therefore ${\tan}^{- 1} \left(- \frac{1}{5}\right) = - \theta$. It follows that ${\tan}^{- 1} \left(- \frac{1}{5}\right)$ is the answer you want. Now use your calculator (in radian mode).