Periodic Function | Glossary - Underground Mathematics

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Glossary

Periodic function Printable version

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”.)

Graph of a repeating wave. The distance between peaks is constant and is labelled T.

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 \(\pi\).

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