Periodic function

We say that a single-variable function $f$ is periodic if for all $x$ , there exists a $p$ such that $f(x + p) = f(x)$ . The smallest positive such $p$ is called the period. The most common examples of periodic functions are the trigonometric functions, such as sine and cosine (and their reciprocal functions cosecant and secant, respectively), which are periodic with period $2\pi$ .