I started with a review of similar triangles, and the proportionality of the sides. Then, I described how to find the point (x, 1/x) for arbitrary x using straightedge and compass. Well, we used higher level tools based on straightedge and compass, such as the construction of a perpendicular to a line through a given point.
I described how to find the point (t, tan(t)) for arbitrary t. We start with constructing an arbitrary arc of the unit circle, call that arc t. Then we use GeoGebra to make the line x=t, and from that point we use constructions based on straightedge and compass.Assignment:
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:
Due: Thursday 3/12 at 5:00 pm.