We have two ways of describing positions on the Cartesian Plane.

\(\blacktriangleright \) Rectangular Coordinates provide left/right and up/down measurements.

\(\blacktriangleright \) Polar Coordinates provide direction and radius measurements.

We can describe Complex numbers with either coordinate system.

We can describe curves with either coordinate system, however, some curves are easier to describe with one coordinate system or the other.

Learning Outcomes

In this section, students will

• use polar coordinates to describe curves.
• convert between polar and Cartesian coordinates.
• convert between the Cartesian and polar representation of a curve.
• determine whether different polar representations represent the same point in the \((x,y)\)-plane.
• use the Cartesian to polar method to plot polar graphs.
• understand the difference between a curve and the choice of coordinates used to describe the curve