# Math

on the rim of the wheel (the rider). Roll the wheel away from the starting point (see figure below) and stop the wheel in at least 16 different positions, including points at which the rider is at the top of the wheel and bottom of the wheel.

At each position, measure the distance from the starting point to the bottom of the wheel (x) and the height (h) of the rider. Care should be taken to make sure that the wheel rolls in a straight line, and that the wheel makes at least one complete rotation. Repeat part 1 three more times, using different starting positions for the rider each time.
Create a table of values and plot the graph of the distance (x) vs. height (h) for each set of data. Which variable should be on the horizontal axis?
Is the graph sinusoidal? Draw a smooth curve through the points.
Using the general equation of the sine function, y = asin [b(x – c)] + d, list as many characteristics as possible (e.g. maxima, minima, symmetry, period, amplitude, phase shift, vertical translation, etc.)
Determine the values of a, b, c, and d in the equation
y = asin [b(x – c)] + d that models the data and matches the graph.
Recall
a = max - min
2
d = max + min
2
Period = 360°
|b|
Phase Shift: c > 0 → shift "c" units to the right.
c < 0 → shift "|c|" units to the left.
Once you have a, b, and d, substitute a point on the curve into the equation to get a value for c.

Determine the radius of the wheel. How does this value relate to the equation?
Find the circumference of the wheel. What is the significance of this value?
Describe how this model of a Ferris wheel differs from a real Ferris wheel. For this model, what does the value of d correspond to? For a real Ferris wheel, would the value of d correspond to the same thing? (Hint: A real Ferris wheel doesn't touch the ground!)
What is the significance of the value of c?
Using the same data, model the movement of the rider using the general cosine function y = acos [b(x – c)] + d. Answer questions 6 to 10 again, using this new equation for reference.
Compare your equations and graphs of the sine and cosine functions, stating any similarities and differences.

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1. for the 2nd part, recall that sin(x) = cos(90°-x) ...

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