Graphs of the Sine and Cosine Functions

Question

A ferris wheel is 35 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

What is the Amplitude?  meters

What is the Midline? y =  meters

What is the Period?  minutes

How High are you off of the ground after 4 minutes?  meters

Answer 1

Amplitude is always the radius of the wheel, which is 17.5 m.

Midline is the distance of the center of the wheel from the height of 0.

That is the radius plus the elevation of the wheel -- 17.5 + 3 = 20.5 m

Period is the time to make one revolution -- 8 min.

After 4 minutes you have completed half a turn.

So if you started at the bottom, then after 4 minutes you will be at the top.

The height of the top is the diameter of the wheel plus the wheel's elevation --

35 + 3 = 38 m

Answer 2

Here is the desmos graph:: https://www.desmos.com/calculator/zvbjzhvcdh