User:Jshflynn/Periodic function

The sine function is an example of a periodic function.

In mathematics, a periodic function is a function which repeats its values regularly like the position of the hands on a clock or the height of a guitar string that has been plucked.

Definition

For a function like $f(x)=2x$ we can divide the domain into blocks of the same size. These are called intervals. For example we might choose to divide the domain of f into blocks of size 3:

...,-4 to -1, -1 to 2, 2 to 5,...

In this case the output of f is different if you choose a different block. There is no block size you can choose that will mean that f repeats itself. This can be seen by looking at the graph of f.

There are functions like $f(x)=\sin(x)$ however which do repeat themselves every or $2\pi$ radians (or 360 degrees) as can be seen by its graph.

$\sin(x)$ is an example of a periodic function.