# How do you find the amplitude and period of a function y= sin(2pix/23)?

Feb 14, 2018

The amplitude is $1$ and the period is $23$.

#### Explanation:

In the general formula

$y = a \sin \left(b \left(x - c\right)\right) + d$,

$a$ is the amplitude and $b$ is the horizontal compression. To calculate the period, divide $2 \pi$ by the $b$ value.

Here's our equation:

$y = \sin \left(\frac{2 \pi}{23} x\right)$

Our amplitude is $1$ because that it the $a$ value.

Here's the calculation for the period:

$\text{period} = \frac{2 \pi}{b} = \frac{2 \pi}{\frac{2 \pi}{23}} = \textcolor{red}{\cancel{\textcolor{b l a c k}{2 \pi}}} \cdot \frac{23}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2 \pi}}}} = 23$