Pre calculus /. Harmonic motion

Question

Find a formula for this function

(2.5,7.2), (?,2.4), (7.5,7.2)

y=(?)cos(2pi/(?)(x-(?))+ (?)

Answer 1

y= Acos(B(x-C))+ D

A= amplitude

B=2pi/Period

C= phase shift

D= midline= average y

(2.5, 7.2), (7.5, 7.2), (5, 2.4)

Period=7.5-2.5=5

B=2pi/5=.4pi

7.2=max, 2.4=min

D=(7.2+2.4)/2=9.6/2= 4.8

A= 4.8/2= 2.4

C=-pi

plug in the values

y= 2.4cos[.4pi(x)+pi] +4.8

Answer 2

Assuming (reasonably) that the two end points are the relative maximums,

the minimum value is at half-way between 2.5 nad 7.5.

that is the value of ?

Sketch a cycle and the values are presented.