Answer:
The function is defined as H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
Step-by-step explanation:
Solution
Let the function be a cosine function
H(t) a cos(b(t+c)) + d
Now,
The maximum height,is H max =12
The minimum height , is H min = 4
The amplitude, a is denoted by
:
a= H max - H min/2
= 12 - 4/2 = 8/2 = 4
Thus,
The vertical shift , d is given by:
d = H max + H min/2
= 12 + 4 /2 = 16/2 = 8
The period T is given by,
T=6.5-1.5=5
So,
b is given by ,
b= 2π /T = 2π/5
The phase shift , c is given by
:
since maximum height occur at 1.5 we get, c=-1.5
Therefore, our function is defined as:
H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
