Question

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.


1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x - d)] + c.
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.

Answer 1

The cosine equation of the attached graph is; y = 5 cos [( π/40)(x - (π/2))] + 3

How to plot a trigonometric graph?

The given parameters are:

Diameter = 10 m

Thus;

Radius; r = 5 m

Time; t = 80 s

Height above the ground, h = 2 m

The above means that:

Amplitude; A = 5 m

Period, T = 80 s

Minimum = 2 m

The cosine function is represented as:

y = a cos [k(x - d)] + c.

where;

A is amplitude

B is cycles from 0 to 2π

period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Thus;

2π/k = 80

k = 2π/80 = π/40

Where

c = Amplitude - Minimum

c = 5 - 2

c = 3

Shift to the left by π/2 gives;

d = π/2

Thus, the equation of the cosine graph is;

y = 5 cos [( π/40)(x - (π/2))] + 3

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