Write an equation of the cosine function with amplitude 3 and period 4π.

Y = 3cos (x/2)

Let your cosine function be y = acos (cx)

Amplitude: a

Period: 2 π/c

If we want to write an equation with an amplitude of 3, we'd just change the a to a 3:

y = 3cos (cx)

Now, since our normal cosine function has a period of 2 π, we can manipulate the inside to have an period of 4π.

2π/c = 4 π

c = 2 π/4 π = 1/2

So, we'd just change c to 1/2 to get our final function:

y = 3cos (x/2)