Question

Hello people ~

Antoine and Adriane are each at the top of a Ferris wheel. After one revolution, each will again be at the top. Which sinusoid (sine or cosine) should you graph to model the ride of your chosen rider? Why? Assume that each Ferris wheel starts at time 't = O' seconds.
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Answer 1

The sine function should be graphed to model the rider's motion on the Ferris wheel because it accurately represents the periodic oscillation of the rider moving from the top to the bottom and back to the top.

Step-by-step explanation:

The sinusoid that should be graphed to model the ride of your chosen rider on the Ferris wheel is the sine function.

A sine function is appropriate because the rider starts at the top of the Ferris wheel, moves down to the bottom, and then returns back to the top. This motion can be represented by the periodic oscillation of the sine function.

The sine function oscillates between +1 and -1 every 2 radians, which corresponds to one full revolution of the Ferris wheel. Therefore, graphing a sine function with the appropriate amplitude and period will accurately model the rider's motion on the Ferris wheel.

Answer 2

graph of cosine function

Step-by-step explanation:

f(x) = sin(x)

The curve of the sine function crosses the y-axis at the origin, heads up to y = 1 at x = π/2 and down to y = -1 at x = 3π/2.

Domain: (-∞, ∞)

Range: [-1, 1]

f(x) = cos(x)

The curve of the cosine function crosses the y-axis at (0, 1) which is its maximum, heads down to y = -1 at x = π then heads up again.

Domain: (-∞, ∞)

Range: [-1, 1]

Given information:

• Antoine and Adriane begin their journey at the top of the Ferris wheel.

• After one revolution, they will again be at the top of the wheel.

If the wheel starts when time t = 0 seconds, and they begin their journey at the top of the wheel (the maximum point), the most appropriate graph to model their ride is the graph of the cosine function since it is at its highest point when x = 0.