Cosine of Angle plus Full Angle/Corollary

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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:

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

$\blacksquare$


Sources