Fitting monthly temperature data to a sine equation

[SvenHoly]

1.
This is the given data table
--------Jan----Feb----Mar---Apr----May----Jun----July----Aug----Sept----Otc----Nov----Dec
Maximum:33.2--32.2--31.2--28.9----25.4----22.2--21.9----23.9----27---- 29.8----31.7----32.9
This is a temperature table and i need to find its sine equation.b3/
y= AsinB(x-C) +D
A=(max-min)/2=(33.2-21.9)/2=5.65
The period is 12 months, so 2pi/B=12 => B= pi/6
D=(max+ min)/2= (33.2+21.9)/2=27.55
C is the half way from the first minimum to the next maximum:
Min: July / 7 Max: January / 13
C=(max+ min)/2=(13 + 7)/2=10
So the equation is: y=5.65sin((pi/6) (x-10))+27.55Well, I want to ask did i do anything wrong?
How to improve this equation to fit the numbers better because the numbers weren't fitted on my graph.
THanks

 

[hotvette]

Let me be the first to welcome you to PF!

OK, you have 4 unknowns (A,B,C,D) and 12 data points. Your teacher gave no hints or clues as to how to approach the problem? What's the name of the class and what are the topics currently being covered?

 

[SvenHoly]

Ah, hi :)
This is an assignment he gave us. It's about sine formula.
As i showed up there: A is the amplitude; B is the period; C is the horizontal translation and D is the horizontal translation.
I worked out the formula for that but the numbers except the maximum and the minimum weren't fitted on the graph perfectly (i used graphic calculator).

So I am looking for a higher maths technique that I haven't studied to improve my formula.
btw, thanks for answering

 

[hotvette]

One technique is least squares, where the objective is to minimize the sum of squares of distances from the data points to the curve. In your case, it's a nonlinear problem since some of the unknowns are within the sin function. You can use Google to get more information.