Workshop on Geometry Software

Math 241
Fall 2015
Professor: Mike O'Sullivan

Here is a summary of what we did this week with details on the assignment. Week 4 Trigonometric Constructions Summary

Week 4: Trigonometry

First Day: Trigonometric Functions and Geometric Constructions

We started with a construction of the points on the hyperbola f(x) = 1/x using tools based on straightedge and compass.

We then moved on to graphing points on the curve f(x) = sin(x).

Assignment:
1. Make a worksheet in which you animate a point on the unit circle and graph the functions sin(x) and cos(x). Explain why your constructions give points on these curves.
2. Make a worksheet in which you animate a point on the unit circle and use the construction of (t, tan(t)) discussed in class to graph the function tan(x). Explain why your constructions give points on these curves.

Second Day: Sums of sine functions and Amplitude Modulation

We used the built in sine function today. We started by graphing f(x)= A*sin(w*x +b) using sliders for A, w, b. We explored the effect of varying each of the parameters: A, the amplitude, w the frequency, and b, which is related to the phase shift (the phase shift is -b/w).

Next we compared sin functions with different frequencies (different values of w) for example sin(x), sin(2*x), sin(3*x). We looked at the sum of the three functions and found the period of the sum. We repeated this for other combinations of sin functions, for example sin(x), sin(x/2), sin(x/3) and sin(x), sin(x/2), sin(x/4). We also explored the impact of using different amplitudes and values for b.

Assignment:
1. Illustrate Amplitude Modulation as discussed on the summary page linked above.