Definition:Pi/Definition 2

Definition
The real number $\pi$ (pronounced pie) is an irrational number (see proof here) whose value is approximately $3.14159\ 26535\ 89793\ 23846\ 2643 \ldots$

The real functions sine and cosine can be shown to be periodic.

The number $\pi$ is defined as the real number such that:


 * the period of both sine and cosine is $2 \pi$.

Also see

 * Equivalence of Definitions of Pi