In this lecture, after answering some homework problems on parametric equations and their graphs, we continue our discussion of polar curves. We use a few more examples to illustrate our method of graphing trig functions in the polar coordinates universe.
We then talk about doing calculus with polar coordinates. As we show, this basically uses the rules we've learned when doing calculus with parametric equations. Since the x- and y-coordinate can be thought of as functions of theta (our parameter). We look at derivatives, horizontal and vertical tangent lines, area, and arc length in the polar universe.
Next time: conic sections!
