A function

*f*is periodic if there is a real positive number*p*so that, for all*x*and (*x*+*p*) of the domain of*f*, we have*f*(*x*+*p*) =*f*(*x*) or*f*(*x*–*p*) =*f*(*x*).Sine, cosine and tangent trigonometric functions are periodic functions.

In the expression “sin (

In the expression “sin (

*x*+*p*)”, the least value of p is the period of the function.### Example

Consider the sine function defined by the relation *f*(*x*) = sin(*x*) = sin(*x* + 2π) which is a periodic function. The period of this function is 2π.