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When is at its maximum value. Since the maximum value of the sine function is , this gives:
When is at its minimum value. So:
Solve these two equations for and . (Easy!)
The time between consecutive high tides, , is the period of the function. This is for the function . So solve the equation
to get the value of .
Finally, the easiest way to get the value of is to work back hours (= time between high time and the time of the mid-point between the tides) to get the value of when the sine function has the value zero, and is increasing.
This give the value hours. So , since this will give the value , when .