Understanding Ferris Wheel Height Function

The video tutorial explains how to graph the height function of a ferris wheel over time. It starts by introducing the function h(t) = 9 - 8cos(18t) and proceeds to graph it over a 30-second interval. The instructor explains the concept of theta and its conversion from time, calculates cosine values for key angles, and plots these points on a graph. The tutorial concludes with a finalized graph and an analysis of the height at specific times.

What is the function of the height of the Ferris wheel in terms of time?

• h(t) = 9 - 8cos(18t)

• h(t) = 8 - 9cos(18t)

• h(t) = 9 + 8cos(18t)

• h(t) = 8 + 9cos(18t)

What is the first step in graphing the function h(theta) = 9 - 8cos(theta)?

• Calculate the cosine values

• Convert time to radians

• Plot the points

• Draw the axes

How do you convert degrees to time in this problem?

• Multiply degrees by 18

• Divide degrees by 18

• Add 18 to degrees

• Subtract 18 from degrees

What is the cosine of 180 degrees?

• 1

• 0

• -1

• 0.5

What is the height of the Ferris wheel when t = 0?

• 17 meters

• 9 meters

• 1 meter

• 8 meters

What was the corrected value for 9 plus 8 in the graph?

• 17

• 16

• 18

• 15

What is the height of the Ferris wheel at t = 10 seconds?

• 1 meter

• 9 meters

• 17 meters

• 8 meters

What is the pattern observed in the graph of the Ferris wheel height?

• Linear

• Exponential

• Sine wave

• Parabolic

What is the approximate height of the Ferris wheel at t = 4 seconds?

• 1 meter

• 17 meters

• 9 meters

• 7 or 8 meters

What is the height of the Ferris wheel at t = 30 seconds?

• 1 meter

• 9 meters

• 17 meters

• 8 meters