Sine of Angle plus Full Angle/Corollary

Theorem
Let $n \in \Z$ be an integer.

Then:
 * $\sin \left({x + 2 n \pi}\right) = \sin x$

Proof
From Sine of Angle plus Full Angle:
 * $\sin \left({x + 2 \pi}\right) = \sin x$

The result follows from the General Periodicity Property:

If:
 * $\forall x \in X: f \left({x}\right) = f \left({x + L}\right)$

then:
 * $\forall n \in \Z: \forall x \in X: f \left({x}\right) = f \left({x + n L}\right)$