Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / 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
Precalculus II / 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

Course: Trigonometry
Topic: Complex, Parametric, and Polar Forms
Subtopic: Parametric 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 parametric equations. Parametric equations are pairs of equations where the x and the y are given as separate functions of time, i.e., x is a function of t and y is a function of t. Both the x and y are given as in x=x(t), y=y(t). As time changes, the coordinates (x,y) will change producing the graph. Parametric equations are particularly useful in the sciences for representing things that change over time.

You can graph parametric curves manually, but it can be tedious. To graph electronically, check if your grapher can graph parametric equations. If you are using a graphing calculator, go to MODE and look for a graphing option called PARAM or PARAMETRIC. Set it on parametric graphing mode, then go to the area where you enter equations to be graphed. Instead of seeing y1, y2, etc., you should see xt1, yt1, xt2, yt2, etc. Now you are ready to go!

Objectives

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

• 9.4.1 Manually graph basic parametric equations by creating a chart of t,x,y values and plotting the (x,y) points for each time t
• 9.4.2 Algebraically eliminate the parameter to convert parametric equations to rectangular equations
• 9.4.3 Electronically graph parametric equations recognizing the starting point and direction of spin
• 9.4.4 Electronically graph parametric equations including lines, circles, ellipses, and parabolas
• 9.4.5 Electronically graph parametric equations that have a shift or translation

Terminology

Terms you should be able to define: parametric point, parametric equation, parameter