CHANGING THE RANGE OF THETA
Because the independent variable (theta) in polar coordinates is fundamentally different from the
x of Cartesian coordinates, the Cartesian x/y ranges can only be used to determine the size of the screen and not the domain of the equation graphed for polar graphs. Although the default 0 to 2pi range is the typical range of theta used for most graphs that go on forever (like spirals) and some closed graphs (like circles), other graphs cannot be completely drawn in this range of theta. For instance, the figure-8-shaped
r^2=64cos(2t), because it is undefined where the right half is less than zero, is missing a couple of spots unless theta's range is extended to -2pi to 2pi. To allow the greatest flexibility, Graphmatica allows theta's range to be changed independently of all other options.
To change the range, select Theta range from the Options menu and enter the start and end of the range you want. For each end of the range, you can specify whether to use radians or degrees by marking the appropriate radio button. (The default is radians.) You can also specify that a number is given as a multiple of pi by marking the "x pi" box of each coordinate.
You can reset the domain to the default (0.0 to 6.28) by pressing the Defaults button.
The Theta Range dialog box can also be obtained by pressing the Change button next to the Theta Range display in the Settings dialog box.
If you would rather not change the default domain but simply change the domain for a single graph, see Specifying a Domain.