The equation of a Tide: with cos or sin?
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?
depth of water during tidal cycles
"It has been shown," said my math instructor, "that most students forget all the trigonometry they learned about a month after the class ends."
One way to answer one of your questions would be to build a table of values for tide highs and lows and times they occurred as would be predicted from your original description, then extrapolate to fill in the water depths between the highs and lows at any increment of time you choose.
Unfortunately a lot of science is grunt work so to speak, going through mounds of data attempting to find a predicatable pattern.
Does the answer in the book predict the the water depth at specifed points?
Does your answer work or not?
Your question presupposes that at least one of the answers is correct. They may both be correct for all I know, or they could both be wrong.
I am not see adept at trigonometry to tell at a glance, or even after long deliberation. Apparently you aren't either, but I am guessing that you are much better at it than I if the first tool you used was trig.