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Period of a Function

Tool to compute the period of a function. The period of a function is the lowest value t such as f(x+t)=f(x-t)=f(x).

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Tag(s) : Mathematics

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# Period of a Function

## Period of a Function Calculator

Tool to compute the period of a function. The period of a function is the lowest value t such as f(x+t)=f(x-t)=f(x).

### How to find the period of a function?

To find the period $$t$$ of a function $$f(x)$$, demonstrate that $$f(x+t)=f(x)$$

Example: $$\sin(x + 2\pi) = \sin(x)$$ so $$\sin(x)$$ is periodic of period $$2\pi$$

Trigonometric functions are usually periodic period, to guess the period, try multiples of pi for value $$t$$.

The value of the period found is also called the periodicity of the function.

If the period is equal to 0, then the function is not periodic.

### How to prove that a function is not periodic?

If $$f$$ is periodic, then it exists a real not null such as $$f(x+t)=f(x)$$ Demonstrate that it is impossible. For example with a reductio ad absurdum or performing a calculation that leads to a contradiction.

### What are usual periodic functions?

The most common periodic functions are trigonometric functions based on sine and cosine functions (which have a period of 2 Pi).