# How do you find the amplitude, period, and shift for y= 4cos(x/2+pi/2)?

Nov 21, 2015

The amplitude is 4, the period is $2 \pi$, and there is an horizontal shift of $- \frac{\pi}{2}$

#### Explanation:

There is a general equation for cosine
$y = a \cdot \cos \left(b \left(x - c\right)\right) + d$
where$| a |$ is the amplitude
$2 \frac{\pi}{|} b |$ is the period
c is the horizontal displacement
and d is the vertical displacement

$| b |$ and $| a |$ mean the value of a or b without the sign ( that is no positive or negative attached to the value)

So for your equation of $y = 4 \cdot \cos \left(\left(\frac{x}{2}\right) + \left(\frac{\pi}{2}\right)\right)$
a = 4
b = 1
$c = - \frac{\pi}{2}$
d = 0
period, $2 \pi$
horizontal displacement $- \frac{\pi}{2}$