Sine and Cosine are Periodic on Reals/Pi/Proof 1

Proof
From the Real Cosine Function is Periodic and Real Sine Function is Periodic, we have that $\cos x$ and $\sin x$ are periodic on $\R$ with the same period.

If we denote the period of $\cos x$ and $\sin x$ as $p$, it follows that $\pi = \dfrac p 2$ is uniquely defined.