Question

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

Answer 1

The amplitude is 4, the period is `2pi`, and there is an horizontal shift of `-pi/2`

Explanation:

There is a general equation for cosine
`y = a*cos(b(x-c)) + d`
where`|a|` is the amplitude
`2pi/|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*cos((x/2) + (pi/2))`
a = 4
b = 1
`c = -pi/2`
d = 0
This makes your amplitude, 4
period, `2pi`
horizontal displacement `-pi/2`
and no vertical displacement