In this section we will be looking at parametric equations and polar coordinates.  While the two subjects don’t appear to have that much in common on the surface we will see that several of the topics in polar coordinates can be done in terms of parametric equations and so in that sense they make a good match in this chapter.

We will also be looking at how to do many of the standard calculus topics such as tangents and area in terms of parametric equations and polar coordinates.

Here is a list of topics that we’ll be covering in this chapter.

Parametric Equations and Curves  An introduction to parametric equations and parametric curves (i.e. graphs of parametric equations)

Tangents with Parametric Equations  Finding tangent lines to parametric curves.

Area with Parametric Equations  Finding the area under a parametric curve.

Arc Length with Parametric Equations  Determining the length of a parametric curve.

Surface Area with Parametric Equations  Here we will determine the surface area of a solid obtained by rotating a parametric curve about an axis.

Polar Coordinates  We’ll introduce polar coordinates in this section.  We’ll look at converting between polar coordinates and Cartesian coordinates as well as some basic graphs in polar coordinates.

Tangents with Polar Coordinates  Finding tangent lines of polar curves.

Area with Polar Coordinates  Finding the area enclosed by a polar curve.

Arc Length with Polar Coordinates  Determining the length of a polar curve.

Surface Area with Polar Coordinates  Here we will determine the surface area of a solid obtained by rotating a polar curve about an axis.

Arc Length and Surface Area Revisited  In this section we will summarize all the arc length and surface area formulas from the last two chapters.