Periodic Functions and Applications

The video tutorial explains the Ferris wheel problem, where a Ferris wheel with a 20-meter radius rotates every 40 seconds. Passengers board at the lowest point, 1 meter above the ground. The tutorial covers sketching the wheel, setting up axes, and understanding amplitude. It introduces two equations to model the wheel's motion, using cosine curves with and without phase shifts. The video demonstrates calculating the height above ground at specific times and finding solutions using Desmos, emphasizing the ease of using a negative cosine curve for certain calculations.

What is the radius of the Ferris Wheel mentioned in the problem?

• 25 meters

• 15 meters

• 20 meters

• 10 meters

How long does it take for the Ferris Wheel to complete one full rotation?

• 60 seconds

• 50 seconds

• 40 seconds

• 30 seconds

At what height do passengers board the Ferris Wheel?

• 2 meters

• 1 meter

• 3 meters

• 0 meters

What is the height of the middle point of the Ferris Wheel?

• 20 meters

• 21 meters

• 41 meters

• 30 meters

What is the total height from the ground to the top of the Ferris Wheel?

• 50 meters

• 41 meters

• 40 meters

• 30 meters

What is the amplitude of the Ferris Wheel's motion?

• 15 meters

• 25 meters

• 20 meters

• 10 meters

What is the vertical displacement of the Ferris Wheel?

• 21 meters

• 20 meters

• 15 meters

• 10 meters

Which type of curve is used to model the Ferris Wheel's motion?

• Exponential curve

• Tangent curve

• Cosine curve

• Sine curve

What is the phase shift applied in the positive cosine curve equation?

• 30 to the right

• 20 to the right

• 40 to the right

• 10 to the right

Why is the negative cosine curve considered easier to work with?

• It is easier to plug into Desmos

• It has a smaller period

• It requires fewer calculations

• It has a larger amplitude