Question

In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0. What are the independent and dependent variables

Answer 1

The independent variable in this scenario is the measurement of time, denoted as x. The dependent variable is the height of the tides, which can be represented by a trigonometric function. For example, let's say we use the sine function to model the height of the tides. The equation can be written as h(x) = A * sin(Bx + C) + D.

Step-by-step explanation:

The independent variable in this scenario is the measurement of time, denoted as x. The dependent variable is the height of the tides, which can be represented by a trigonometric function.

For example, let's say we use the sine function to model the height of the tides. The equation can be written as:

h(x) = A * sin(Bx + C) + D

• A represents the amplitude of the tides, in this case, 6 feet.
• B represents the frequency of the tides, which determines the time period for a complete cycle. In this scenario, since there are two high tides and two low tides in one day, the time period would be 12 hours, or 0.5 units if we use the x variable.
• C represents the phase shift, which determines the starting point of the cycle. Since the first high tide occurs at x = 0, there is no phase shift.
• D represents the vertical shift, which determines the average sea level. In this scenario, the average sea level is 0 feet.

Therefore, the equation to model the height of the tides using a trigonometric function would be:

h(x) = 6 * sin(0.5x)

Answer 2

Answer: The "independent variable" is the "time" (in hours) that is plotted on the "x-axis". Note the "time" (in hours) can be "manipulated" in the sense that is it "chosen" by the humans who are measuring the data (e.g. when to start, how many hours, and at what intervals.

The "dependent variable" is the measurement (in feet) above or below the sea level, and this is plotted on the "y-axis". These values cannot be "manipulated" in the sense that one cannot "choose" what value or measurement the tide level would be at any particular time.

Hope these answers—and explanations—are of help to you.
Best wishes!