Arctangent of Zero is Zero

Theorem

 * $\arctan 0 = 0$

Proof
By definition, $\arctan$ is the inverse of the tangent function's restriction to $\displaystyle \left({-\frac \pi 2 \,.\,.\, \frac \pi 2}\right)$.

By Tangent of Zero, we have $\tan 0 = 0$.

As $\displaystyle 0 \in \left({-\frac \pi 2 \,.\,.\, \frac \pi 2}\right)$, we have $\arctan 0 = 0$ by the definition of an inverse function.