Question

1. ) compare the amplitude of y=1.5sin(4x) to the amplitude of y=sin x

2.) compare the period of y=1.5sin(4x) to the period of y=sinx

please help!​

Answer 1

Figure is shown for graph of y=1.5sin4x

The equation of sin function is given as
`y=Asin((2\pi)/(T) x )`

Where A is Amplitude of function and T is Time period

Given sin function is
`y=1.5sin(4x )`

A) Compare the amplitude of y=1.5sin(4x) to the amplitude of y=sin x

Ans

In y=sin x, Amplitude is 1 unit

In y=1.5sin4x, Amplitude is 1.5 unit

B) compare the period of y=1.5sin(4x) to the period of y=sinx

In y=sin x, Time period is

`(2\pi)/(T) x =x`

T =
`2\pi`

In y=1.5sin4x, Time period is

`(2\pi)/(T) x =4x`

`T =(2\pi)/(4)`

`T=(\pi)/(2)`

C) Plot the graph for 2 period

Shown in figure.