# State the amplitude and period of this function: y = 4sin(1/2)x ?

Jun 20, 2018

$\text{amplitude "=4," period } = 4 \pi$

#### Explanation:

$\text{given the sine function in the form}$

•color(white)(x)y=asinbx

$\text{amplitude "=|a|," period } = \frac{2 \pi}{b}$

$\text{here } a = 4 , b = \frac{1}{2}$

$\text{amplitude "=|4|=4." period } = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

Jun 20, 2018

Amplitude is 4

Period is $4 \pi$

#### Explanation:

The parent function is:

$y = \sin x$

this function has a amplitude of $1$ and a period of $2 \pi$

graph{y=sinx [-10, 10, -5, 5]}

Standard equation for sin is:

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

a = amplitude (vertical stretch/compression)

b = horizontal stretch/compression

c = horizontal shift

d = vertical shift

$y = 4 \sin \left(\frac{1}{2}\right) \left(x\right)$

$a = 4$

$b = \frac{1}{2}$

So that cuts the input values and half doubling the period.