Question

At an ocean depth of 20 meters, a buoy bobs up and then down 2 meters from the ocean's depth. Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0, the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Answer 1

The first and second coordinate points of the sine graph are;

(0, 20) and (2, 22)

Sine Graph expression

The general formula we will use to plot the graph is;

y = [Asin (2πx/t)] + ∅      (Note that sin is in radians)

where;

A is amplitude

t is period

∅ is phase shift

We are told that the buoy bobs up and then down 2 meters from the ocean's depth. This means that;

Amplitude; A = 2

Now, Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Thus;

Period = 2 * 4 = 8 seconds

Assume at x = 0, the buoy is at normal ocean depth. Thus;

Phase shift; ∅ = 20

Thus, we have;

y = [2sin((2πx/8)] + 20  

At x = 0, we have;

y = [2sin((2π*0/8)] + 20  

y = 0 + 20

y = 20

Thus, first point is; (0, 20)

Since the second point must be a maximum or minimum value on the graph closest to the first point, then we put 2 for x to get the coordinate of the second point;

y = [2sin((2π*2/8)] + 20  

y = [2sin((2π*2/8)] + 20  

y = [2sin(π/2)] + 20  

In radians, sin(π/2) = 1. Thus;

y = (2 * 1) + 20

y = 22

Second point is (2, 22)

Using the first and second point coordinates, we will use sine tool to graph the function as attached below.

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