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

Oct 10, 2015

Amplitude=3
Period=4 $\pi$
Phase shift= $\frac{\pi}{2}$

#### 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 $2 \frac{\pi}{\omega}$
To find the phase shift you use $\frac{\Phi}{\omega}$

$2 \pi$/$\frac{1}{2}$ =$4 \pi$

$\frac{\pi}{4}$/$\frac{1}{2}$=$\frac{\pi}{2}$

Divide the period by 4 to get the 4 sections of the graph.
$4 \frac{\pi}{4}$=$\pi$

Start your first point on the graph using the phase shift, which is $\frac{\pi}{2}$ to the right (if the equation was + $\frac{\pi}{4}$ 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= $\frac{\pi}{2}$.