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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).

Answers to Questions

How to find the period of a function?

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

\( \sin(x + 2\pi) = \sin(x) \) so \( \sin(x) \) is periodic

The most common periodic functions are trigonometric functions based on sine and cosine functions (that have a 2 pi period), so you can try multiples of pi.

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 $$ f(x+t)=f(x) $$ One has to demonstrate that it is impossible. For example with a reductio ad absurdum or performing a calculation that leads to a contradiction.

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