AS/A2 Pure 5 Pure 6

P4 Topic 7: Polar Coordinates
r2 = cos(at)
Investigate polar curves with equations of the form r2 = cos(at) for various values of a. Pay close attention to any loops or symmetry or occurances of cusps. You may have to zoom out to get a better view. Click the left button to zoom in. Use Shift-click to zoom out. Click and hold down the right button to drag the graph.

Summary Clearly, curves with equations of the form r2 = cos(at) have a loops. They have symmetry about the x and y axes. Based on free Java applets from JavaMath