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.

Determine these key features of the function that models the tide:

1.amplitude
2.period
3.frequency
4.midline
5.vertical shift
6.phase shift

Answer 1

1. The amplitude of the function is 12 feet, since it moves from 6 feet above to 6 feet below the average sea level.

2. The period of the function is 12 hours, since it takes 12 hours for the tide to go from high to low and back again.

3. The frequency of the function is 0.5 (1/12), since it takes 12 hours for the function to repeat itself.

4. The midline of the function is the average sea level.

5. There is no vertical shift.

6. The phase shift is 0, since the first high tide occurs at x = 0.