Properties of the Real Tangent Function

Theorem: Image of the Real Tangent Function

The image of the real tangent function is $(-\infty ;+\infty )$.

PROOF

TODO

Theorem: Periodicity of the Real Tangent Function

The real tangent function has a period of $\pi$. More generally,

$\tan (x+k\pi )=\tan (x)\forall k\in \mathbb{Z}$

PROOF

TODO