# Periodic function

A function is called periodic if it repeats itself over and over again at regular intervals.

Formally, a function $f$ is periodic with period $T$ (where $T>0$) if $f(x+T)=f(x)$ for all $x$. The smallest such positive $T$ is called the least period (or often just “the period”) of the function. (If $f$ is a constant function, then it is periodic with every possible period, but it doesn’t have a “least period”.)

For example, $\sin x$, $\cos x$ and $\tan x$ are all periodic. For $\sin x$ and $\cos x$, the (least) period is $2\pi$, while for $\tan x$, the (least) period is $\pi$.