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

Sep 9, 2016

Use the form $y = A \sin \left(B x - C\right) + D$

#### Explanation:

$y = A \sin \left(B x - C\right) + D$

$\left\mid A \right\mid$ = amplitude
$\frac{2 \pi}{B}$ = period
$\frac{C}{B}$ = phase shift
$D$ = vertical shift

$y = - \sin \left(x - \pi\right)$

In this example, $A = - 1$ and $\left\mid A \right\mid = 1$ so the amplitude is 1.

Period = $\frac{2 \pi}{B} = \frac{2 \pi}{1} = 2 \pi$

Phase shift = $\frac{C}{B} = \frac{\pi}{1} = \pi$ to the right. A negative sign in the parentheses means shift right.

To graph, one complete sine curve must be $2 \pi$ "wide" because the period is $2 \pi$. 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.