# How do you determine the amplitude, period and the phase shift period of y=-4sin(6pix+3pi)?

Apr 22, 2015

Have a look at your function:

it is in the form:
$y =$-(Amplitude)$\sin \left(k x + \phi\right)$

Your amplitude is $4$ so that your function will oscillate between $+ 4$ and $- 4$;

$k = 6 \pi$ but $k$ is related to the period as: $k = \frac{2 \pi}{p e r i o d}$
So your period will be: $\frac{1}{3}$;

The Phase Shift is $\phi = 3 \pi$

Graphically: