The new and improved Screamer should start at (0,50) and have a lowest point at y=- 150.
Example Solution: y=100cos x-50
Practice makes perfect
Let's illustrate the new and improved Screamer.
Since the center of the Screamer is 50 feet below ground and the radius of the wheel is 100 feet, the graph's highest point must be 50 feet up in the air, and the lowest point must be - 150 feet below ground. The passenger gets on the ride when x=0, so the function starts at (0,50).
As the Screamer turns, the Passenger will start dropping towards the ground. After a while, the passenger goes below ground until it reaches the lowest point 150 feet below ground after having traveled half a circle.
Having passed the lowest point, the Screamer will start moving towards the ground until it reaches its highest point 50 feet up in the air. At this point, it will have completed one lap.
Writing the function
Now we have to write a function that fits the curve we created. Notice that we are free to choose y=sin x or y=cos x as a parent function. This is because they are translations of each other. However, since the function of y=cos x starts at its highest point, which is similar to our graph, we will use this as our parent function.
If we examine y=cos x, we see that it has an amplitude of 1 while the function we want to create has an amplitude of 50+(- 150)2=100. Therefore, to obtain the correct amplitude we have to multiply our parent function by 100. Let's plot this new function in the same graph as the graph describing the Screamer.
Finally, to map y=100cos x onto the graph describing the Screamer, we have to vertically translate it down by 50 units.
