# How do I determine the amplitude, period, and phase shift for this function? y=-2cos(pi/2x+pi)

Mar 20, 2018

When given an equation of the form $y = A \cos \left(B x + C\right) + D$:

$\text{Amplitude} = | A |$

$\text{Period} = \frac{2 \pi}{|} B |$

$\text{Phase shift} = - \frac{C}{B}$

$\text{Vertical shift } = D$

#### Explanation:

Using above information on the given equation, $y = - 2 \cos \left(\frac{\pi}{2} x + \pi\right)$:

$\text{Amplitude} = | - 2 |$

$\text{Amplitude} = 2$

$\text{Period} = \frac{2 \pi}{|} \frac{\pi}{2} |$

$\text{Period} = 4$

$\text{Phase shift} = - \frac{\pi}{\frac{\pi}{2}}$

$\text{Phase shift} = - 2$