### Home > INT3 > Chapter Ch9 > Lesson 9.2.1 > Problem 9-101

The CPM Amusement Park has decided to imitate *The Screamer* but wants to make their ride even better. Their ride will consist of a circular track with a radius of 100 feet, and the center of the circle will be 50 feet under ground. Passengers will board at the highest point, so they will begin with a blood-curdling drop. Write a function that relates the angle traveled *from the starting point* to the height of the rider above or below the ground. Homework Help ✎

Begin by sketching a unit circle to model the situation.

When the passenger boards at 90° on the unit circle (but 0° traveled), they are

50 feet above ground.

Make a table of values then sketch the graph.

Determine the parameters of the equation.

As with any periodic function, either *y* = sin*x* or *y* = cos*x* could be the parent graph for the equation.

Since we have started at a high point, we will use cosine as the parent.

Determine the horizontal and vertical shifts and the amplitude.

The horizontal shift (*h*) is 0. The vertical shift (*k*) is 50 feet down. The amplitude (*a*) is 100.

Substitute the parameters into the general equation, *y* = *a* · sin(*x* − *h*) + *k*.

Use a graphing calculator to see that your equation matches your graph.