Arctangent of Zero is Zero

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Theorem

$\arctan 0 = 0$


Proof

By definition, $\arctan$ is the inverse of the tangent function's restriction to $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.

By Tangent of Zero:

$\tan 0 = 0$

As $0 \in \openint {-\dfrac \pi 2} {\dfrac \pi 2}$, we have $\arctan 0 = 0$ by the definition of an inverse function.

$\blacksquare$