We were given a data table listed as the following:

Time Depth (ft)
12am 9.8
1am 11.4
2am 11.6
3am 11.2
4am 9.6
5am 8.5
6am 6.5
7am 5.7
8am 5.4
9am 6.0
10am 7.0
11am 8.6
12am 10.0

we were asked to make a scatter plot of the data which I did, and then we were asked to find both a sin and a cosine equation that models the data, and I have no idea how to do that... we were also asked what the depth of the water will be at 10:45am? I would greatly appreciate it if anyone could explain how to go about solving this problem, thank you in advance...

Well, I guess you can say you're lucky that I roam the boards these days... I don't want to do all the work, so I'll just give you a start. First, you want to use radians, and not degrees, to find the period of the function. You should know that the equation should look something like this:

y=Asin[2*pi*x/B + *phi*] + c where A is the amplitude, phi is the phase shift, c is some constant, and B is the period. (maybe it's somewhat different, use whatever your book gives you)

Since you know where the approximate crests and troughs are of the function, you can find where the initial point of the sine function would be with a phase shift of zero. (you take the average of the high and low points)

To convert to cosine, you just add pi/2 to the phase shift you calculated for the sine, and you have the cosine function.

This should be the framework you need to solve your problem. I'll stick around, so if you have any other comments/additions/questions, I'll be glad to answer them.

Dr. Calc ;)