### Home > INT3 > Chapter 9 > 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.

Begin by sketching a unit circle to model the situation. When the passenger boards at

When they have traveled

After traveling

After moving

They return to

Make a table of values then sketch the graph.

Determine the parameters of the equation.

As with any periodic function, either or

*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 *k*) is *a*) is

Substitute the parameters into the general equation, .

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