Circular Graphs: Vehicles for Conic and Polar Connections

A unified treatment of conic sections and polar equations of conics can be found in most calculus books where the reciprocals of limafçons are shown to be conic sections. The treatment, however, is from an algebraic standpoint and does not refer to the inherent connection between polar graphs and the graphs of trigonometric functions and conics. Beginning with information gained from the graphs of circular functions of the form y = A + B sin x, students can be guided to graph conic sections on the polar plane without using a table of values. This approach helps students to appreciate the roles that both algebra and coordinate geometry play in weaving various sections of mathematics into a meaningful whole.