Question

How do you graph `y = -3sin (1/2x - pi/4)`?

Answer 1

Amplitude=3
Period=4 `pi`
Phase shift= `pi/2`
With reflection about the x-axis.

Explanation:

y=Asin( `omega` x- `phi`)
The (-) before the A indicates a reflection about the x-axis
A is amplitude in absolute value |A|
To find the period for sin you use `2pi/omega`
To find the phase shift you use `Phi/omega`

`2pi`/`1/2` =`4pi`

`pi/4`/`1/2`=`pi/2`

Divide the period by 4 to get the 4 sections of the graph.
`4pi/4`=`pi`

Start your first point on the graph using the phase shift, which is `pi/2` to the right (if the equation was + `pi/4` the shift would be left) . From there, each section is over by `pi` and don't forget the reflection.

You may find it easiest to make each tick mark on the x-axis= `pi/2`.