A [i]periodic function[/i] is a function that repeats at regular intervals. For example, the time of day repeats with a period of 24 hours. The interval of repretition is called the function's [i]period[/i], and has the symbol [math]P[/math].[br][br]For any periodic function, [math]f(x)=f(x+P)[/math], meaning that the value of [math]f[/math] at any point [math]x[/math] is the same as the value any whole number [math]n[/math] of periods before or after [math]x[/math].

Choose one of the three trig functions by clicking the box next to the function name. Sine and Cosine have a period of [math]2\pi[/math], while Tangent has a period of [math]\pi[/math].[br][br]The blue Period bar has a length of one Period of [math]f[/math]. Thus, it reaches from a point on the graph [math](x, f(x))[/math] to a point 1 period away, [math](x+P,f(x+P))[/math]. For any such point [math]x[/math], [math]f(x)=f(x+P)[/math] because [math]f[/math] is periodic.