# Periodic Formulas

A function is defined as a relation which possesses one output value for each permissible or allowable input value. The period of a function is the number “T” such that so, if a number is fixed and $\theta$ is any angle, we have the following below given period. The function sine and cosine have a period 2$\pi$.

Some of the trigonometry periodic functions are given below,

$\large Sin\left(\omega\theta\right)\Rightarrow T=\frac{\pi}{\omega}$

$\large Cos\left(\omega\theta\right)\Rightarrow T=\frac{\pi}{\omega}$

$\large Tan\left(\omega\theta\right)T=\frac{\pi}{\omega}$

### solved examples

Question 1: Find the period of the function $cos$ $\frac{x}{3}$?

Solution:

Let y = $cos$ $\frac{x}{3}$

Use period formula,

T = $\frac{2\pi}{\omega}$

The multiple of x = $\frac{1}{3}$ = ${\omega}$

T = $\frac{2\pi}{\frac{1}{3}}$ = 6$\pi$

Hence the period of the function $cos$$\frac{x}{3}$ is 6$\pi$