Suppose that the length of time between consecutive high tid

Suppose that the length of time between consecutive high tides is approximately 12.5 hours. According to the National Oceanic and Atmospheric Administration, on a particular day in a city in Georgia, high tide occurred at 3:34 AM (3.5667 hours) and low tide occurred at 10:04 AM (10.0667 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.4 feet and the height of the water at low tide was - 0.4 foot. Answer parts (a) through (c) below. (a) Approximately when will the next high tide occur? (b) Find a sinusoidal function of the form y = A sin (omega x -) + B that fits the data.

Solution

a) First high tide occured at 3:34 am (3.5667 hr)

Next high tide would be at 3.5667 +12.5 = 16.0667 hrs = 4:04 pm

b) high tide = 8.4 ft ; low tide = -0.4 foot

Mean level = 4.4 ft

Amplitude = 4ft

B = 2pi/ period = 2pi/12.5 = 0.16pi

At x = 3.5667 ; ; y = 8.4ft

So, y = Asin(wx +phi) +B

8.4 = 4sin(0.16pi *3.5667 +phi) +4.4

1 = sin(0.16pi *3.5667 +phi)

pi/2 = 0.57pi* +phi

phi = -0.07pi

So, y = 4sin(0.16pi*x - 0.07pi) + 4.4