The purpose of the PolarPlot tool is to allow you
to visualize functions of angle plotted on an x-y plane.
The function value is computed as radial distance,
and plotted as a curve of x-y points.

Fundamentals

Enter your function in the box provided below the graph
as a function of the variable theta. Press the plot
button to see the plot of your function.

Features

Options exist to let you change the range of theta visualized,
change the bounds of the display, add an offset to the function value,
change the number of points used in the plot, add a trace of past
function displays, and color the plot by whether the value is
positive (red) or negative (blue).

Things to try

What functions of theta are really periodic over a range of
0 to 2 pi? Plot the function

f(theta) = sin(0.5*theta)

from 0 to 2 pi. Does f(0) = f (2 pi)?

What if you use different upper and lower limits? What
about plotting f(theta) from -pi to pi? Do you get the same picture?

Suppose you use the function

f(theta) = sin(2*theta)

from -pi to pi, and 0 to 2 pi. Is this function really periodic
over the range 0 to 2 pi? Is sin( 2 * theta ) =
sin( 2 * ( theta + 2 pi ) )? How many functions can you find for
which this is true?