# Periodic Functions **A periodic function is a function whose graph contains a pattern which is repeated at regular intervals.** [[Trigonometric Functions]] are the most commonly used periodic functions in mathematics. The length of the smallest repeating pattern of a periodic function is called the _period_. The _midline_ of a periodic function is a line $y=c$ that cuts the function in half. The _amplitude_ of a periodic function is the function's maximum deviation from the midline i.e. the height of one of its peaks. Given a $\cos$ function $f(x) = a\cos (bx) + d$ the function's properties are as follows: - Period: $P = \frac{2\pi}{|b|}$ - Midline: $M = d$ (because $\cos$ is already centered around the $x$ axis, the midline is the $x$ offset) - Amplitude: $A = |a|$