The CPM Amusement Park has decided to imitate The Screamer but wants to make it 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
They return to
Make a table of values then sketch the graph.
Determine the parameters of the equation.
As with any periodic function, either
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
Substitute the parameters into the general equation,
Use a graphing calculator to see that your equation matches your graph.