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Algebra
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Well, how far did you get?
-20cos[4xpi/25] will give you low tide at 9:15 (x=0) and high tide at 3:30 (x=6.25), but the next low tide will be at 9:45 (x=12.5), since the period is 12.5 rather than 12. I don't know if it's even possible to make a function with one cosine that goes from min to max in a different time than it goes from max to min, it seems like you would need multiple trig functions for that.
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