The question says to create an equation to describe the depth of water as a function of time. The description of the tide goes like this:
The wter depth in a harbour is 8 m at low tide and 20 m at high tide. One cycle is completed every 12 hours.
The question asks us to "Find an equation for the water depth, d(t) meters, as a function of time (t) hours, after high tide, which occured at 03:00 .
What I know from this is that the amplitude is 6 m. Since we are finding the tide relative to high tide, we can use cos as our function, correct? Then our period (lets say k) equals 2(pi)/k=12hours, and we work that out to be pi/6 .
So in my attempt, I came up with the equation: d(t)=6cos((pi)/6)t+12
The back of the book gives different. Can anyone explain what I did wrong?