Chapter 11: Polar and Parametric Functions

Chapters 1 through 8 focused on functions in rectangular form (based on the xy−plane). With functions in rectangular form, you now can find the slope at any point (if it exists) and can calculate the area under the curve.

However, calculus can also be applied to other forms of equations as well. This chapter is devoted to developing calculus tools for other forms of equations: polar, parametric, and vector.

Two-dimensional motion will also be analyzed with the help of velocity and acceleration vectors.

Chapter Goals

Calculate areas bounded by polar
curves.

Calculate slopes and lengths
of parametric curves.

Study velocity and acceleration
vectors.

Chapter Outline

Section 11.1

You will develop a method to calculate the area bounded by a polar curve or two polar curves. You will write an integral expression that represents the area of a region that is contained by a polar curve.

Section 11.2

You will calculate slopes and arc lengths of parametric curves. You will compute velocity, acceleration, speed and total distance traveled for particles moving in an xy‑plane.

Section 11.3

You will develop two methods to determine the slope of a line tangent to a polar curve at a point.

Section 11.4

You will apply your knowledge of parametric functions and their derivatives to simulate a robot competition and determine the winner.