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The cosine function for the ferris wheel ride is an illustration of a sinusoidial function
The equation of the Ferris wheel is y = -190cos(π / 120 t) + 195
A cosine function is represented as:
y = Acos(Bt - C) + D
From the complete question, the diameter of the ferris wheel is 380 feet.
The amplitude represents the radius, and this is calculated as:
A = 380/2
A = 190
The function becomes:
y = 190cos(Bt - C) + D
The period of the function is:
T = 2π / B
From the complete question, one full rotation is completed in 4 minutes.
Convert the time to seconds
T = 4 * 60
T = 240.
So, we have:
240 = 2π / B
Divide both sides by 2
120 = π / B
Make B the subject
B = π / 120
The function becomes
y = 190cos(π / 120 t - C) + D
From the question, the ferris wheel is 195 feet above the ground.
This represents the vertical shift.
So, we have:
D = 195
The function becomes
y = 190cos(π / 120 t - C) + 195
Also, we have:
The lowest point is at t = 0 and the function is a negative cosine function
So, we have:
C = 0
The function becomes
y = -190cos(π / 120 t) + 195
Hence, the cosine function is y = -190cos(π / 120 t) + 195
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