Question

How do you use transformation to graph the sin function and determine the amplitude and period of `y=sin(3x)`?

Answer 1

See below.

Explanation:

We can find the transformation of `sin(x)` to `sin(3x)` using the following equation:

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

Where:

Amplitude is `color(white)(88)a`

Period is `color(white)(88)(2pi)/b`

Phase shift is `color(white)(88)(-c)/b`

Vertical shift is `color(white)(88)d`

`:.`

For `color(white)(88)y=sin(3x)`

Amplitude is 1, (This is the same as `sin(x)`)

Period is `color(white)(88)(2pi)/b=(2pi)/3` ( period of `sin(x)` is `2pi`)

( This is a compression in the horizontal direction by a factor of 3 )

Phase shift is `color(white)(88)(-c)/b=0/3=0` ( No phase shift )

Vertical shift is `color(white)(88)d=0` ( No vertical shift )

Graph of `y=sin(x) and y=sin(3x)`