Sine and Cosine are Periodic on Reals

Theorem
The sine and cosine functions are periodic on the set of real numbers $\R$:

Cosine and Sine have Equal Period

 * SineCos.png

Note
Given that we have defined sine and cosine in terms of a power series, it is a plausible proposition to define $\pi$ using the same language.

$\pi$ is, of course, the famous irrational constant $3.14159 \ldots$.