In bear creek bay in july, high tide is at 1: 00 pm. the water level at high tide is 7 feet at high tide and 1 foot at low tide. assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for bear creek bay's water level in july as a function of time (t).

Ok, let's set up a few variables:

W = Water Level (In Feet)

t = Time on the clock

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The model you are looking for is in fact:



You must place the time 1:00pm underneath the angle (3/2)*π radians.

Each hour that goes by is equivalent to (1/2)*π radians.

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TABLE OF VALUES:

When t=0, W=4 [10am]

When t=0.5π, W=5.5 [11am]

When t=π, W=6.6 [12pm]

When t=1.5π, W=7 [1pm]

When t=2π, W=6.6 [2pm]

When t=2.5π, W=5.5 [3pm]

When t=3π, W=4 [4pm]

When t=3.5π, W=2.5 [5pm]

When t=4π, W=1.4 [6pm]

When t=4.5π, W=1 [7pm]

When t=5π, W=1.4 [8pm]

When t=5.5π, W=2.5 [9pm]

When t=6π, W=4 [10pm]

When t=6.5π, W=5.5 [11pm]

When t=7π, W=6.6 [12pm]

When t=7.5π, W=7 [1am]

etc... etc...

*The information above demonstrates that high tides only shape up every 12 hours.