# I know arctan (-1) = 3pi/4 but does it also equal 7pi/4?

Sep 11, 2015

...or, alternatively "No"

#### Explanation:

In order to be treated as a function (which means it can not map into more than one value)
the range of $\arctan$ is restricted.

The most common version is that
$\textcolor{w h i t e}{\text{XXX}} - \frac{\pi}{2} < \arctan \left(\theta\right) \le \frac{\pi}{2}$
although you will see
$\textcolor{w h i t e}{\text{XXX}} 0 \le \arctan < \pi$

The second version is the one you refer to initially
$\textcolor{w h i t e}{\text{XXX}}$(otherwise $\arctan \left(- 1\right) = - \frac{\pi}{4}$)
but for neither version is $\frac{7 \pi}{4}$ within the defined range.