# How do you determine the Amplitude, period and phase shift for y = 1/2 sin(x + pi)?

Jul 1, 2015

$y = a \sin \left(b x + c\right)$

#### Explanation:

Has
Amplitude = $\left\mid a \right\mid$, in this case Amplitude = $\frac{1}{2}$

Period = $\frac{2 \pi}{b}$, in this case Period = $\frac{2 \pi}{1} = 2 \pi$

You can learn a formula for Phase Shift, but I never use one. To find the phase shift, solve $b x + c = 0$

In this case $x + \pi = 0$ at $x = - \pi$, so Phase Shift = $- \pi$