# How do you calculate the arctan(0)?

Nov 21, 2015

$\arctan \left(0\right) = 0$

#### Explanation:

$\arctan \left(0\right)$ is at which at which x $\tan \left(x\right) = 0$
and $- \frac{\pi}{2} < x < \frac{\pi}{2}$
(or $- 90 < x < 90$ if you use degrees)

$\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$
$\tan \left(x\right) = 0$
when
$\sin \left(x\right) = 0$

Use the attached unit circle from wikipedia:

$x = 0 + n \cdot 2 \cdot \pi$
or
$x = \pi + n \cdot 2 \cdot \pi$
so in this case
$x = n \cdot \pi$
where n is an integer
Only x = 0 satisfies
$- \frac{\pi}{2} < x < \frac{\pi}{2}$

$\sin \left(0\right) = 0$
$\tan \left(0\right) = 0$
$\arctan \left(0\right) = 0$