Question

PLEASE HELP!

Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.

Answer 1

Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.

Answer 2

Explanation:

A possible trigonometric function that would model the tide situation for this beach is:

h(t) = -2 + 3sin(πt/12)

where h(t) represents the height of the tide at time t in hours, and πt/12 represents the angle (in radians) corresponding to the time t on a unit circle with a period of 24 hours.

The constant -2 represents the lowest point of the tide (2 feet below sea level), and the coefficient of 3 in front of the sine function determines the amplitude of the tide, which is 3 feet (half the difference between the highest and lowest points of the tide, which is 4 - (-2) = 6 feet). The sine function oscillates between -1 and 1, so the range of the function h(t) is between -2 - 3 = -5 feet (when the sine function takes on its minimum value of -1) and 4 - 2 = 2 feet (when the sine function takes on its maximum value of 1), as expected for the given tidal range.