Question

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

Answer 1

`"amplitude "=4," period "=4pi`

Explanation:

`"given the sine function in the form"`

`•color(white)(x)y=asinbx`

`"amplitude "=|a|," period "=(2pi)/b`

`"here "a=4,b=1/2`

`"amplitude "=|4|=4." period "=(2pi)/(1/2)=4pi`

Answer 2

Amplitude is 4

Period is `4pi`

Explanation:

The parent function is:

`y=sinx`

this function has a amplitude of `1` and a period of `2pi`

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

Standard equation for sin is:

`y=asin(bx-c)+d`

a = amplitude (vertical stretch/compression)

b = horizontal stretch/compression

c = horizontal shift

d = vertical shift

`y=4sin(1/2)(x)`

`a = 4`

`b = 1/2`

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