# How do you graph and list the amplitude, period, phase shift for y=-sin(pix+1)-2?

Mar 17, 2018

I use the online graphing calculator Desmos. You merely enter the function $y = - \sin \left(\pi x + 1\right) - 2$ and it produces very nice graphs that can be exported:

This is a good reference for Graphing Trigonometric Functions

When given a sine function of the form:

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

The amplitude is $| A |$

In the case of, $y = - \sin \left(\pi x + 1\right) - 2$, the amplitude is $| - 1 | = 1$

The period is:

$\tau = \frac{2 \pi}{|} B |$

$\tau = \frac{2 \pi}{\pi}$

$\tau = 2$

The phase shift is:

$\phi = - \frac{C}{B}$

$\phi = - \frac{1}{\pi}$