PolarCurves

This applet shows the connection between a curve described in polar coordinates, r and theta, given as r = f(theta) and the graph of the (r, theta) pairs which satisfy this relationship plotted in a polar coordinate system.

Within the rectangular system, x represents theta and f(x) is r. You can change the expression for f(x) by double clicking it in the left hand pane under "Free Objects" and editing it. Once you've done this, you can drag the point on the blue curve (the graph of r = f(theta)) and see how the corresponding (r, theta) pair is plotted in polar coordinates. The red curve is the set of all possible (r, theta) pairs and is therefore the graph of r = f(theta) in polar coordinates. Also, try dragging the blue curve around in the coordinate system and observe how it affects the polar graph. In particular observe the changes in the polar graph when you make a horizontal translation (phase change) of the blue curve and when you make a vertical translation of the blue curve.

Gary Church, Created with GeoGebra