Polar coordinates - investigate curves

Resources on the web:

• Famous curves applet index from MacTutor History Archive - draw lots of different curves and see the equivalent cartesian equation.
• Classic curves by Paul Bourke - a description of some common curves.
• Visual Dictionary of Special Plane Curves by Xah Lee - includes movies and Geometer SketchPad files.

Points to consider when investigating polar curves:

• What happens to the shape of the curve if I change this number to ... ?
• What angles are required to draw the whole curve?
• Can I explain the shape of the curve by looking at the polar equation?
• Could I convert the equation from polar form to cartesian form (can be tricky)?

Make a note of your findings including sketches of graphs. Comment on the effect of changing the values of the parameters; consider negative as well as positive values, non-integer as well as integer values.

Find the equation for each of the curves:

• worksheet
• answers