A periodic function is a function that repeats its outputs at regular intervals, forming a definite pattern. The cycle of a periodic function is the shortest repeating portion of the graph, and the period is the horizontal length of one cycle. More precisely, a function $f(x)$ is said to be periodic if a non-zero constant $P$ exists such that $f(x+P)$ and $f(x)$ have the same value if and only if both $x$ and $x+P$ are in the domain.

Two well known examples of periodic functions are the trigonometric functions $f(x)=\sin x$ and $g(x)=\cos x,$ both with a period of $2\pi$ radians.

In the following applet, the graphs of $f(x)=\sin x$ and $g(x)=\cos (x)$ can be seen. Note that the domain of each function is in radians, not in degrees.