# Periodic Function

Function `y=f(x)` is called **periodic** if exists such number `T!=0` that for any `x` from domain of the function `f(x+T)=f(x)`.

From the definition it follows that periodic function has infinitely many periods. If `T` is period of function then any number of the form `kT`, where `k` is integer,is also period of function.

Often (but not always) among set of positive periods of the function we can find the smallest one. This period is called **main period** (or simply **period).**

For example trigonometric function `y=sin(x)` has period `2pi` because `sin(x+2pi)=sin(x)` for all `x`.