# How do you evaluate cot(arctan (3/5))?

May 28, 2016

$\frac{5}{3}$

#### Explanation:

Let $a = a r c \tan \left(\frac{3}{5}\right)$. Then, $\tan a = \frac{3}{5}$.

So, the given expression is $\cot a = \frac{1}{\tan a} = \frac{5}{3}$.

May 28, 2016

$\frac{5}{3}$

#### Explanation:

Use the fact that $\cot \left(x\right) = \frac{1}{\tan} \left(x\right)$ to show that

$\cot \left(\arctan \left(\frac{3}{5}\right)\right) = \frac{1}{\tan} \left(\arctan \left(\frac{3}{5}\right)\right)$

Note that $\tan \left(x\right)$ and $\arctan \left(x\right)$ are inverse functions—namely, $\tan \left(\arctan \left(x\right)\right) = x$ and $\arctan \left(\tan \left(x\right)\right) = x$.

So, the tangent and arctangent functions in the denominator will cancel one another out, leaving only $\frac{3}{5}$:

$\frac{1}{\tan} \left(\arctan \left(\frac{3}{5}\right)\right) = \frac{1}{\frac{3}{5}} = \frac{5}{3}$