# How do you find the amplitude and period of y=4sintheta?

Jan 1, 2017

The amplitude is $4$ and the period is $2 \pi$.

#### Explanation:

Find the amplitude and period of $y = \textcolor{red}{4} \sin \theta$.

A sine function can be written as $y = A \sin \left(B x - C\right) + D$

where $A$ is the amplitude

$\frac{2 \pi}{B}$ is the period

$\frac{C}{B}$ is the phase shift and

$D$ is the vertical shift.

This example, $y = 4 \sin \theta$, may be be written as
$y = \textcolor{red}{4} \sin \textcolor{b l u e}{1} \theta$ where
$A = \textcolor{red}{4}$ and $B = \textcolor{b l u e}{1}$

The amplitude is $\textcolor{red}{4}$ and the period is $\frac{2 \pi}{\textcolor{b l u e}{1}} = 2 \pi$.