Sine and Cosine Functions

Question

A Ferris wheel has a diameter of 60 feet. When you start at the top of the Ferris wheel, you are 62 feet from the ground. The Ferris wheel completes one rotation in 2 minutes. 

1. 1. Create a graph that represents your height relative to the center of the Ferris wheel as a function of time, using the image below as a guide. Replace the image with your graph.
2. 
3. 2. Create a function that represents your height relative to the center of the Ferris wheel as a function of time.

Answer 1

What a super question Anessa!

Luckily you know the question is about sine and cosine functions, so really all you have to do is decide if you are going to draw a sine curve or a cosine curve! If you recall, sine curves start at 0 height at 0 degrrees, rising to their maximum at 90 degrees, and back to 0 at 180 degrees. While a cosine curve is shifted, it is already at maximum at 0 degrees, and falls to 0 at 90 degrees, then is negative maximum at 180 degrees.

Which one do you need to pick? The clue is that you "start at the top of the ferris wheel".

Now get your drawing skills ready (I hate drawing cosines and sines), and sketch the curve on the graph... just making you sure you draw enough curve until it starts to repeat.

That's the hard work done!

All that's left is to put some numbers on the two axes. Normally, a sine/cosine curve graph is marked in degrees horizontally, and values vertically (between 1 and -1).

In your case, the x axis is time instead, while the y axis is height in feet.

For time, the problem tells you the wheel completes one rotation in 2 minutes. That means you are back at the top. Where are you at one minute? Now you can mark 1 and 2 on your x axis.

For the y axis, you should mark the maximum height, and the minimum height. The problem says "relative to the center of the Ferris wheel". So be careful, and think for a moment, because the problem says "diameter of 60 feet" and "62 feet from the ground" which might trick some people. Think radius, and relative to the center, and you won't get caught out.