Refer to the figure shown below.
From midnight (high tide) to 6 AM (low tide) is 6 hours, and it is half the period.
Therefore the period is
T = 12 hours.
Half the difference between 10 ft and 6 ft is the amplitude.
The amplitude is
A = 3 ft
On a graph of x versus t, where x = height (ft) after t hours, the mathematical model is
[tex]x(t)=3cos( \frac{ \pi t}{6})+7 \,ft \\ where\\ t=time,\, hours [/tex]
The graph of the mathematical model agrees with the illustrated sketch, as shown.
