Difference between revisions of "Periodic function"

m (trig functions)
 
Line 1: Line 1:
We say that a single-variable [[function]] <math>f</math> is '''periodic''' with period <math>p</math> if for all <math>x</math>, <math>f(x + p) = f(x)</math>. The most common examples of periodic functions are the [[trigonometric function]]s, such as [[sine]] and [[cosine]] (and their [[reciprocal function]]s [[cosecant]] and [[secant (trigonometry)|secant]], respectively), which are periodic with period <math>2\pi</math>.
+
We say that a single-variable [[function]] <math>f</math> is '''periodic''' if for all <math>x</math>, there exists a <math>p</math> such that <math>f(x + p) = f(x)</math>. The smallest positive such <math>p</math> is called the period.  The most common examples of periodic functions are the [[trigonometric function]]s, such as [[sine]] and [[cosine]] (and their [[reciprocal function]]s [[cosecant]] and [[secant (trigonometry)|secant]], respectively), which are periodic with period <math>2\pi</math>.
  
 
{{stub}}
 
{{stub}}

Latest revision as of 14:47, 21 August 2011

We say that a single-variable function $f$ is periodic if for all $x$, there exists a $p$ such that $f(x + p) = f(x)$. The smallest positive such $p$ is called the period. The most common examples of periodic functions are the trigonometric functions, such as sine and cosine (and their reciprocal functions cosecant and secant, respectively), which are periodic with period $2\pi$.

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS