Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

Course: Trigonometry
Topic: Complex, Parametric, and Polar Forms
Subtopic: Polar Equations and Graphs

Overview

Ready to learn a whole new way to graph? Instead of graphing functions in the form y=f(x), in this lesson we graph polar equations. Polar equations which are (usually) given as r as a function of theta, r=r(θ). These equations relate r, the distance from the origin, to the central angle theta. As we increase theta, we spin around the origin, and while doing so the distance from the origin to the curve can change essentially pushing the curve away from the origin or pulling it in toward the origin.

You can graph polar curves electronically or manually on "polar graphing paper". Check if your grapher can graph polar equations. If you are using a graphing calculator, go to MODE and look for a graphing option called POL or POLAR. Also, you usually want to be in RADIAN mode, but it depends on your window settings. Now go to the area where you enter equations to be graphed. Instead of seeing y1, y2, etc., you should see r1, r2, etc. You are ready to go!

Objectives

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

• 9.5.1 Convert rectangular points to polar points, and visa versa
• 9.5.2 Convert rectangular equations to polar equations, and visa versa using x=rcostheta, y=rsintheta, r=sqrt(x^2+y^2), theta=tan^-1(y/x)
• 9.5.3 Plot polar points on the polar plane
• 9.5.4 Manually graph basic polar equations on the polar plane including lines and circles
• 9.5.5 Electronically graph polar equations including ellipses, lemniscates, cardioids, limacons, roses, and spirals
• 9.5.6 Identify a given polar curve as a circle, ellipse, lemniscate, cardioid, limacon, or rose

Terminology

Define: polar plane, polar point, polar equation, lemniscate, cardioid, limacon, rose

Supplementary Resources

Optional reading with plenty of "how to graph" examples: Graphing Five Classic Polar Curves

An interesting application of polar graphs: Polar Coordinates and Cardioid Microphones