Test your function r = R(theta) by making a polar plot for theta
between - 2 pi and 4.5 pi, with equal scales in the horizontal
and vertical directions. The result should look something like the outer spiral
curve in Part 2.
Find parametric equations,
x = x(theta) and y = y(theta) to describe the same curve. Plot
the parametric equations to confirm that you really have the same curve.
Change the left end of the
theta interval from - 2 pi to - 10 pi, and plot again.
How does this change the graph?
Zoom in on the graph several
times until you are looking at parts of it much closer to the origin. What
do you notice? (If you need to, use values of theta smaller than -
10 pi.)
Usually when you zoom in on
a continuous curve, you see a very different behavior than you have just seen
with the equiangular spiral. What is that different behavior?