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Mathematics LibreTexts

4.3: Periodic Functions

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We first need to define a periodic function. A function is called periodic with period p if f(x+p)=f(x), for all x, even if f is not defined everywhere. A simple example is the function f(x)=sin(bx) which is periodic with period (2π)b. Of course it is also periodic with periodic (4π)b. In general a function with period p is periodic with period 2pchar3B.png3pchar3B.png…. This can easily be seen using the definition of periodicity, which subtracts p from the argument

f(x+3p)=f(x+2p)=f(x+p)=f(x).

The smallest positive value of p for which f is periodic is called the (primitive) period of f.

Exercise 4.3.1

What is the primitive period of sin(4x)?

Answer

π2.


This page titled 4.3: Periodic Functions is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Niels Walet via source content that was edited to the style and standards of the LibreTexts platform.

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