# How do you evaluate cot[arccos (-4/5)] ?

##### 1 Answer
Oct 12, 2016

$\cot \left[\arccos \left(- \frac{4}{5}\right)\right] = - \frac{4}{3}$

#### Explanation:

$\cot \left[\arccos \left(- \frac{4}{5}\right)\right]$-->restriction for $\arccos x$ is $\left[0 , \pi\right]$.

Since the argument is negative that means our triangle is in quadrant two with the adjacent side -4 and hypotenuse 5. Hence this is a 3-4-5 triangle with the opposite side being 3.

Therefore $\cot \theta$ = adjacent/opposite = $\frac{a}{o} = - \frac{4}{3}$