# How do you simplify arctan (-1)?

Nov 10, 2015

$\arctan \left(- 1\right) = - \frac{\pi}{4}$

#### Explanation:

If $\theta = \arctan \left(- 1\right)$
then
$\textcolor{w h i t e}{\text{XXX}} \tan \left(\theta\right) = - 1$

$\Rightarrow$ for a triangle in standard trigonometric position
$\textcolor{w h i t e}{\text{XXX")("opposite")/("adjacent}} = - 1$

and since $\arctan$ is defined as having a limited range of $\left(- \frac{\pi}{2} , + \frac{\pi}{2}\right]$

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