Question

How do you graph and list the amplitude, period, phase shift for `y=-sin(x-pi)`?

Answer 1

Use the form `y=Asin(Bx-C)+D`

Explanation:

`y=Asin(Bx-C)+D`

`abs(A)` = amplitude
`(2pi)/B` = period
`C/B` = phase shift
`D` = vertical shift

`y=-sin(x-pi)`

In this example, `A=-1` and `absA = 1` so the amplitude is 1.

Period = `(2pi)/B = (2pi)/1 = 2pi`

Phase shift = `C/B = pi/1=pi` to the right. A negative sign in the parentheses means shift right.

To graph, one complete sine curve must be `2pi` "wide" because the period is `2pi`. And, a phase shift of `pi` to the right means the beginning of the sine curve should start at `pi`. Also, note the negative in front of the sin. That means the graph should be flipped over the x axis.