# Periodic Formulas

function is described as relation that has one output value for every permissible or possible input value. The number “T” is the period of a function. If the number is fixed and $\theta$ is an angle we have the following periodic formula. The function sine and cosine have a period 2$\pi$. Some of the trigonometry periodic functions are given below: $\large Sin\left(\omega\theta\right)\Rightarrow T=\frac{2\pi}{\omega}$ $\large Cos\left(\omega\theta\right)\Rightarrow T=\frac{2\pi}{\omega}$ $\large Tan\left(\omega\theta\right)T=\frac{\pi}{\omega}$

### Solved Example

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

Solution: Let y = $cos$ $\frac{x}{3}$

Using the 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$\pi$.