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 (x + p)”, the least value of p is the period of the function.
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.