Periodicity of Trig Functions

A periodic function 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 period, and has the symbol . For any periodic function, , meaning that the value of at any point is the same as the value any whole number of periods before or after .
Choose one of the three trig functions by clicking the box next to the function name. Sine and Cosine have a period of , while Tangent has a period of . The blue Period bar has a length of one Period of . Thus, it reaches from a point on the graph to a point 1 period away, . For any such point , because is periodic.