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:
[tex]W=3\cos { \left( \frac { 1 }{ 3 } t-\frac { \pi }{ 2 } \right) } +4[/tex]
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.
