President's Problems

We continue the President's Problems, with problems posed by Karl Zilm. If you wish, you may send proposed solutions to Karl at Lewis & Clark. His address is in the mailing list earlier in this issue. This problem is one of a pedagogical nature.

Pedagogical Problem: One of my colleagues had an interesting thing happen one day in a Tech Math class. They were studying trigonometric functions and examining the function

f(x)=5sin(60x + 3.8), where the angle is measured in radians. The class determined the amplitude, period, and shift and determined that they could graph one period on their graphing calculators by graphing the function for x in the interval [-.063,.041]. Most of the students graphed the function using the endpoints of this interval for Xmin and Xmax and got the expected graph. One student, however, graphed this function on her TI-82 using Xmin=0 and Xmax=10. She got a graph which seemed to indicate that the function had a very different period from the one which had been computed earlier. A quick check indicated that the equation was correctly entered, and, other than having a different choice for Xmin and Xmax, all calculator settings were appropriate (e.g., radian mode).

a) Why does the calculator appear to display a graph with a much larger period than the true period of the function when graphed on [0,10]?

b) If this happened to one of the students in your class, how would you use this situation as a constructive educational opportunity for your students?