You are here
Homeexamples of periodic functions
Primary tabs
examples of periodic functions
We list common periodic functions. In the parentheses, there are given their period with least modulus.

Oneperiodic functions with a real period:
sine ($2\pi$), cosine ($2\pi$), tangent ($\pi$), cotangent ($\pi$), secant ($2\pi$), cosecant ($2\pi$), and functions depending on them – especially the triangularwave function ($2\pi$); the mantissa function $x\!\!\lfloor{x}\rfloor$ (1).

Oneperiodic functions with an imaginary period:
exponential function ($2i\pi$), hyperbolic sine ($2i\pi$), hyperbolic cosine ($2i\pi$), hyperbolic tangent ($i\pi$), hyperbolic cotangent ($i\pi$), and functions depending on them.

Twoperiodic functions: elliptic functions.

Functions with infinitely many periods:
the Dirichlet’s function
$\displaystyle f\!:\;x\mapsto$ $\displaystyle\left\{\begin{array}[]{ll}1&\mbox{when}\,\,x\in\mathbb{Q}\\ 0&\mbox{when}\,\,x\in\mathbb{R}\!\smallsetminus\!\mathbb{Q}\end{array}\right.$ has any rational number as its period; a constant function has any number as its period.
Mathematics Subject Classification
30A99 no label found26A09 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
new question: Prime numbers out of sequence by Rubens373
Oct 7
new question: Lorenz system by David Bankom
Oct 19
new correction: examples and OEIS sequences by fizzie
Oct 13
new correction: Define Galois correspondence by porton
Oct 7
new correction: Closure properties on languages: DCFL not closed under reversal by babou
new correction: DCFLs are not closed under reversal by petey
Oct 2
new correction: Many corrections by Smarandache
Sep 28
new question: how to contest an entry? by zorba
new question: simple question by parag