Question

How do you use transformation to graph the sin function and determine the amplitude and period of `y=3sin(1/2x)-2`?

Answer 1

The amplitude is 3 and the period is `4\pi`

Explanation:

One way to write the general form of the sine function is
`Asin(B\theta+C)+D`

A = amplitude, so 3 in this case

B is the period and is defined as `Period = {2\pi}/B`

So, to solve for B, `1/2 = {2\pi}/B->B/2 = 2\pi-> B=4\pi`

This sine function is also translated 2 units down on the y axis.