Cosine of Angle plus Full Angle/Corollary

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

Then:
 * $\map \cos {x + 2 n \pi} = \cos x$

Proof
From Cosine of Angle plus Full Angle:
 * $\map \cos {x + 2 \pi} = \cos x$

The result follows from the General Periodicity Property:

If:
 * $\forall x \in X: \map f x = \map f {x + L}$

then:
 * $\forall n \in \Z: \forall x \in X: \map f x = \map f {x + n L}$