# Math Help - High Tide, Low Tide

1. ## High Tide, Low Tide

The water depth in a harbour is 12 m at high tide and 11 m at low tide. One cycle is completed approximately every 12 hours. Find an equation for the water depth as a function of the time.

I am very confused on how we would find out the equation, and I have already tried with the amplitude and period. PLEASE HELP!!

2. let d = water depth

$d = A\sin(Bt) + D$

amplitude ... $A = \frac{12-11}{2} = \frac{1}{2}$

$B = \frac{2\pi}{T} = \frac{2\pi}{12} = \frac{\pi}{6}$

mean height, $D = \frac{12+11}{2} = \frac{23}{2}$

$d = \frac{1}{2}\sin\left(\frac{\pi}{6} t\right) + \frac{23}{2}$