Sinusoidal functions of real-world data

 Date March 2006 Class Advanced Math Teacher Alicia Klaassen Notes Sinusoidal functions of real-world data Process:  We are learning about the sine and cosine functions in our advanced math class.  We have been studying how the equations of sinusoidal functions change when the graphs are shifted up and down and left and right and amplitude changes and period changes.  We have also really been working on using radian measure for our x-axis.  So the activity was to use what our book calls “real-world” data and model it by using a sine or cosine function.  Our real world data was average temperature during a certain month in a US city.  The students were to find: phase shift, amplitude, period, vertical shift and create the equation.  We did several examples. Then using the calculator and a sine regression function we found the best equation to model the situation (or data points).  After the students were somewhat comfortable with both methods, I sent them on their way to do some similar book problems for an assignment.  Of course, one of the students was checking their answer in the back of the book and saw that the book had a cosine function were we had a sine function.  That led to a really wonderful discussion about how a sine graph and a cosine graph can look exactly the same.  Next year, this discussion will be a planned discussion and example.  Instead of letting the students find out by chance, I will make sure that they discover it through some examples instead. Overall, I feel like the activity was a great success!