📂Functions

Periodic Function

Definition

A function $f : \mathbb{R} \to \mathbb{R}$ is called a $T$-periodic function if it satisfies the following for some constant $T \ne 0$ and for all $t \in \mathbb{R}$: $$f(t + T) = f(t)$$

Example

Sine $\sin$ and cosine $\cos$ are typical periodic functions, and according to the above definition, they are $2\pi$-periodic functions.