How do you find the amplitude, period, and shift for y=4cos(x2+π2)?

1 Answer
Nov 21, 2015

The amplitude is 4, the period is 2π, and there is an horizontal shift of π2

Explanation:

There is a general equation for cosine
y=acos(b(xc))+d
where|a| is the amplitude
2π|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=4cos((x2)+(π2))
a = 4
b = 1
c=π2
d = 0
This makes your amplitude, 4
period, 2π
horizontal displacement π2
and no vertical displacement