Math 326, March 19 -
Polar Graphs
We graph equations in polar coordinates as in 5.2. We start
by graphing
r = a + bcos(ct)
We convert this polar equation into a Cartesian plot using the
conversion formulas
x = rcost, y = rsint
The angle variable t should
increase in small steps and span several periods; say 400 steps of
0.02*PI() to start which will give us a 4*2pi range.
Additional Questions
- Add second series to the graph which traces along with the
help of a
scroll bar. Also include a reference line from the end of the
tracing graph to the origin.
- Make a second, separate graph which plots r against t (so not in polar anymore).
Add an animated tracing series to this graph as well, connected to the
same scroll bar as the polar tracing series. Include a reference
line from the end of the tracing graph down to the x-axis.
- Change a, b and c to create the following shapes:
- Cardioid: r = a + acost
- Limaçon: r = a + bcost with b > a
- Copy and adjust your model to create the following shapes from
parametric equations:
- Astroid: x = cos3t, y = sin3t
- Deltoid: x = a(2 cost + cos2t), y = a(2 sint - sin2t)
- Cycloid: x = a(t
- sint), y = a(1 - cost) (shape
traced by a point on a wheel)
- Try adding an animated rolling wheel to your Cycloid graph to
show how the curve is traced. (Difficult)