you will need the period
high tide = 2:0 am
low tide = 6:00 am
time between is 4 hrs, which is half the period
(to get the full period you would go from high to low (4hrs) and back to high again(another 4 hrs)
period = 8
2π/k = 8
8k = 2π
k = 2π/8 = π/4
so you have y = 6 cos (π/4)t + h , the height
remember the min of the equation we have so far is -6, but we want that to be 8 , so we have to raise the curve 14 m
y = 6 cos (π/4)t + 14
need : y = 6cos (π/4)(t + d) + 14
we know that at t=2 , y = 20
20 = 6 cos (π/4)(2-d) + 14
cos (π/4)(2-d) = (20-14)/6 = 1
but we know cos 0 = 1
so (π/4)(2-d) = 0
d=2 , but I just noticed you already had that
y = 6 cos (π/4)(t-2) + 14
check for other data:
at 6:00 am , h = 8 ---- t=6 should give us y = 8
y = 6 cos (π/4)(6-2) + 14
= 6 cos (π) + 14
= 6(-1) = 14 = 8
looks like we nailed it
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