# How do you find the amplitude and period of y= 1/4 sin x?

Jul 22, 2015

The period of $y = \frac{1}{4} \sin \left(x\right)$ is $2 \pi$
The amplitude of $y = \frac{1}{4} \sin \left(x\right)$ is $\frac{1}{4}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$(that is $y \epsilon \left[- \frac{1}{4} , + \frac{1}{4}\right]$)

#### Explanation:

The period of $\sin \left(x\right)$ is $2 \pi$
Multiplying $\sin \left(x\right)$ by a constant only stretches the graph vertically by whatever that constant is; it does not change (for example) the points at which $\sin \left(x\right)$ returns to $0$.

As noted above, multiplying $\sin \left(x\right)$ by a constant stretches it's value by that constant.
Since the range of $\sin \left(x\right)$ is $\left[- 1 , + 1\right]$
$\textcolor{w h i t e}{\text{XXXX}}$the range of $\frac{1}{4} \sin \left(x\right)$ is $\left[- \frac{1}{4} , + \frac{1}{4}\right]$
$\Rightarrow$ an amplitude of $\frac{1}{4}$