# How do you find the period and frequency of a sine function?

Jul 14, 2018

The period is $= 2 \pi$ ad the frequency is $= \frac{1}{2 \pi}$

#### Explanation:

The period $T$ of a periodic function $f \left(x\right)$ is

$f \left(x\right) = f \left(x + T\right)$

Here,

$f \left(x\right) = \sin x$............................$\left(1\right)$

Therefore,

$f \left(x + T\right) = \sin \left(x + T\right)$

$= \sin x \cos T + \cos x \sin T$...........................$\left(2\right)$

Comparing equations $\left(1\right)$ and $\left(2\right)$

$\left\{\begin{matrix}\cos T = 1 \\ \sin T = 0\end{matrix}\right.$

$\implies$, $T = 2 \pi$

The period is $= 2 \pi$

The frequency is

$f = \frac{1}{T} = \frac{1}{2 \pi}$

graph{sinx [-3.75, 16.25, -5, 5]}