Modeling Temperature
The sine curve is a periodic function that repeats itself. The shape of the curve is similar to the shape of waves in an ocean. A graph of the sine curve is shown below.
The monthly average of the mean temperature (in degrees F) in Athens, GA from 1990  1997 is shown in the table below.
January 
44.4 
February 
48.3 
March 
54.0 
April 
61.7 
May 
70.0 
June 
76.7 
July 
79.7 
August 
78.8 
September 
73.3 
October 
62.7 
November 
52.3 
December 
46.9 

The data are graphed (blue diamonds) in an Excel spreadsheet. On the spreadsheet you will notice the following cells just above the graph:
A= 
1.000 
B= 
1.000 
C= 
1.000 
D= 
1.000 

A, B, C, D correspond to the equation: Temperature = A*sin (B*month + C) + D. This is the equation with which we will model the actual temperature data above. A mathematical model is a representation of a phenomenon using mathematics. The values of this equation is graphed (pink squares). Change the numerical values of the variables until the model closely resembles the actual data.
Why is the sine curve used to model the temperature data? What is the equation that best modeled the temperature? What happens to the sine curve when you change the values of A, B, C, and D?

Extensions 
Compare and contrast yearly maximal temperature fluctuation patterns in different cities. Examine the same data set from the national weather service in California or Utah.
Submit your idea for an investigation to InterMath.
