# How do you find the exact value of cot (arctan (5/8))?

Mar 24, 2016

$\frac{8}{5}$

#### Explanation:

Recall that $\cot \left(x\right) = \frac{1}{\tan} \left(x\right)$. Thus,

$\cot \left(\arctan \left(\frac{5}{8}\right)\right) = \frac{1}{\tan} \left(\arctan \left(\frac{5}{8}\right)\right)$

$\tan \left(x\right)$ ard $\arctan \left(x\right)$ are inverse functions, so $\tan \left(\arctan \left(x\right)\right) = x$ and $\tan \left(\arctan \left(\frac{5}{8}\right)\right) = \frac{5}{8}$.

So, we obtain:

$\frac{1}{\tan} \left(\arctan \left(\frac{5}{8}\right)\right) = \frac{1}{\frac{5}{8}} = \frac{8}{5}$