Draw the graph representing High and low tide from midnight. Make a trigonometric function that describes the high and low tide behavior from midnight.

Question

a beach has reported its high tide to be at a depth of 58ft and its low tide to be at a depth of 2 ft. High tide occurs at 6:30 am while low tide occurs 6 hours and 12 minutes after high tide. Draw the graph representing the high tide and low tide from midnight. Make a trigonometric function that best describes the high and low tide behavior from midnight, Find the depth of the water at noon. And at what time after 2pm could a boat needing 25 ft of water to board come in and dock?

Answer 1

high tide 58 feet deep, low tide 2 feet deep

high tide 6:30 am, low tide 6 hours and 12 minutes after high tide = 12:42 pm same day

trig function that fits, find water depth at noon. after 2pm, what time could a boat dock that needs 25 feet of water to come in

fit the data to f(x) = Asin(Bt+C) +D where A =Amplitude = (max-min)/2= (58-2)/2 = 56/2 = 28, B = pi/period, C = phase shift, D = midline = (max+min)/2 = average depth = (58+2)/2 = 60/2 = 30

y = f(x) = depth = 28sin(pit/6.7 +0) + 30

for t=0, depth = 28(0) + 30 = 58 for 6am. t=0 means 6 am

noon means t = 0+5.5 = 5.5

5.5 = 28sin(pit/6.7) + 30, solve for t than add 5 hours 30 minutes

25 = depth = 28sin(pit/6.7) +30

solve for t

-5/28 = sin(pit/6.7)

pit/6.7 = arcsin(-5/28)

t = (6.7/pi)arcsin(-5/28)

then add 5 hours and 30 minutes