Comparing the Regions of Polar and Cartesian Graphs

This Demonstration uses trigonometric curves to show the differences between regions of polar and Cartesian graphs. The left side of the Demonstration shows the Cartesian graph and its region, and the right side shows the polar graph and its region. You can choose among different trigonometric curves to see the differences between the polar and Cartesian graphs. The values of are restricted to where the graph of the polar equation does not overlap itself. There is no simple correspondence between the areas of the two regions.