Properties of the Real Sine Function

Theorem: Parity of the Real Sine Function

The real sine function is :

$\sin (-x)=-\sin (x)$

PROOF

TODO

Theorem: Image of the Real Sine Function

The image of the real sine function is $[-1;1]$.

$\sin (\mathbb{R})=[-1;1]$

PROOF

TODO

Theorem: Periodicity of the Real Sine Function

The real sine function has a period of $2\pi$. More generally,

$\sin (x+2k\pi )=\sin (x)\forall k\in \mathbb{Z}$

PROOF

TODO

Theorem: Antiperiodicity of the Real Sine Function

The real sine function has an antiperiod of $\pi$. More generally,

$\sin (x+(2k+1)\pi )=-\sin (x)k\in \mathbb{Z}$

PROOF

TODO