In one area of the Bay of Fundy, the tides cause the water level to rise to 7.2 m above average sea level and to drop to 7.2 m below average sea level. The time between the peak and the trough is approximately 6 hours. Determine the equation of a sinusoidal function that would model this situation assuming that at t=0 the trough of the tide is 2m.

Answer 1

the amplitude is clearly 7.2, so start with

y = 7.2 cos(kt)

The period is 2*6=12 hours, so k = 2π/12 = π/6

y = 7.2 sin(π/6 t)

Now we are stuck. The tide starts at 2m, but is that on the way down, or the way up? And how can that be the trough? The trough is at -7.2m.

Anyway, assuming you just mean that y(0) = 2, let's assume that the tide is rising then. That means
sin(π/6 t) = 2/7.2, so t=0.28

Shifting the graph to the left, that gives

y = 7.2 sin(π/6 t + 0.28)

http://www.wolframalpha.com/input/?i=7.2+sin(%CF%80%2F6+t%2B0.28)+for+-1%3Ct%3C12