# How do you calculate arctan(1)?

Nov 28, 2015

$\arctan \left(1\right) = \frac{\pi}{4} \left(= {45}^{\circ}\right)$

#### Explanation:

$\arctan$ is by definition a value in the range $\left(- \frac{\pi}{2} , + \frac{\pi}{2}\right)$

If $\arctan \left(1\right) = \theta$
then $\tan \left(\theta\right) = 1$

This means that a standard trigonometric triangle will have opposite and adjacent sides of equal length.
(since by definition $\tan = \left(\text{opposite")/("adjacent}\right)$)

$\Rightarrow \theta = \frac{\pi}{4}$