Write a cosine function that has a midline of y=5, an amplitude of 3 and a period of 3

Answer 1

f(x) = Acos(Bx+C)+D is general formula

with

A = Amplitude = 3 = (max-min)/2

B=frequency = 2pi/period = 2pi/3

C = phase or horizontal shift=0

D = midline = 5 = average y = (max+min)/2

plug those values into the formula

f(x) = 3cos(2pix/3)+5

Answer 2

General form of a cosine function:

f(x)=Acos(Bx-C)+D

Amplitude A=3

Midline D=5

Period P=3 B=?

P=2pi/B; 3=2pi/B; B=2pi/3

f(x)=3cos((2pi/3)x)+5

Answer 3

y = Acos(Bx + C) + D

A = amplitude = 3

2π/B = period = 3. So, B = 2π/3.

D = vertical shift = 5 (the midline is y = 5)

-C/B = horizontal shift. Since there is no horizontal shift, C = 0.

y = 3cos[ (2π/3)x] + 5