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 2π 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.