Question

Fitzgerald Marine Reserve is a great place to go tidepooling, if you go near low tide. At 12:00am on September 4, 2018 (midnight, right after September 3 ended, with September 4 just beginning), there was a high tide of 3.5ft. The first low tide after that point was at 7am on September 4, 2018, with a depth of 0.5ft.

1. Assuming the tides in Half Moon Bay follow a simple sinusoidal model, write a formula for H(t), the water’s height t hours after 12:00am on September 4, 2018. Your work should include listing the amplitude, midline, and period.

2. Sketch at least one full period of the graph of H(t) on the grid below. Draw the axes and choose the scale so that your function fills up most of the graph. Clearly label any important features.

3. Find the window of time on this date for which the water’s depth is greater than (2- (3sqrt(3)/4)) feet. Give exact times in HH:MM am/pm form, like 11:15am to 12:30pm. Show complete work, without using a calculator.

Answer 1