examples of periodic functions

We list common periodic functions. In the parentheses, there are given their period with least modulus.

One-periodic functions with a real period:
sine (2π), cosine (2π), tangent (π), cotangent (π), secant (2π), cosecant (2π), and functions depending on them – especially the triangular-wave function (2π); the mantissa function x−⌊x⌋ (1).
One-periodic functions with an imaginary period:
exponential function (2iπ), hyperbolic sine (2iπ), hyperbolic cosine (2iπ), hyperbolic tangent (iπ), hyperbolic cotangent (iπ), and functions depending on them.
Two-periodic functions: elliptic functions.
Functions with infinitely many periods:
the Dirichlet’s function
${ 1 when x ∈ ℚ f : x ↦→ 0 when x ∈ ℝ\ ℚ$

has any rational number as its period; a constant function has any number as its period.

"examples of periodic functions" is owned by pahio.
(view preamble)