Graphing Polar Equations

This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented. Points in polar coordinates are represented by (R , t) where R is the polar distance and t is the polar angle. The method of point-by-point is used here. Free polar graph paper is available.

Examples on Graphing Polar Equations with Solution

Example 1

Graph the polar equation given by
R = 4 cos t
and identify the graph.

Solution to Example 1


Example 2

Graph the polar equation given by
R = 2 + 2 sin t
and identify the graph.
Solution to Example 2

Example 3

Graph the polar equation given by
R = 4 cos 2t
and identify the graph.

Solution to Example 3

More References and Links to Polar Coordinates

Polar Coordinates.