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Periodic Function

Concept

Periodic Function

A function is said to be periodic if its values repeat at regular intervals. More precisely, a function f(x)f(x) is said to be periodic if, there exist a nonzero constant PP such that

f(x+P)=f(x)f(x+P)=f(x)

for all values of xx in the domain. The constant PP is called the period or fundamental period of the function, if it is the smallest positive real number satisfying the condition shown above.
A well known example of periodic functions are the trigonometric functions which have a period of 2π.2\pi. Some examples are shown below.

sin(x+2π)=sin(x)cos(x+2π)=cos(x)\begin{gathered} \sin(x+2\pi)=\sin(x)\\ \cos(x+2\pi)=\cos(x) \end{gathered}

Here, the arguments of the tigonometric functions is in radians not in degrees.