LESSON NOTES MENU
 
Course: Calculus II
Topic: Parametric, Polar, and Conic Curves
Subtopic: Polar Equations and Curves

Overview

Recall from a Pre-Calculus course polar equations (see Lesson Notes - Trigonometry - Polar Equations and Graphs but ignore any "text notes"). A polar equation, e.g. `r=sin(3theta)`, can be converted to a rectangular equation, but some calculus operations may be simplified by working with the polar form. This lesson merely reviews and practices skills working with polar coordinates, polar equations, and polar curves from a Pre-Calculus course in preparation for doing calculus in polar coordinates in the next lesson.

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Terms you should be able to define: polar equation, pole, collision point, self-intersection point

Mini-Lectures and Examples

STUDY: Polar Coordinates, Equations, and Curves

Supplemental Resources (recommended)

Common Polar Curves is a simple sheet from Prof. Kate Niedzielski, Univ. of Minnesota. However, this sheet is weak on limicons, so for those I would refer instead to MathWords >> Limacon which includes a limacon with a "loop", a limacon with a "dimple", and a convex ("flattened") limacon. Watch out though, MathWords swaps the `a` and `b` in the equations of a limacon compared to other sources. Explore the various limacons via DESMOS interactively and watch for the relationships between `|a/b|<1`, `|a/b|=1`, `1<|a/b|<2`, `|a/b|>=2`.

Supplemental Resources (optional)

The material below reviews concepts from Pre-Calculus.

Video: Polar Coordinates and Graphs, Selwyn Hollis's Video Calculus

Lesson: Polar Coordinates, Dale Hoffman's Contemporary Calculus

rev. 2021-02-28