Parametric Equations: another process to describe a plane curve on the Cartesian coordinate system. 11.1 – Parametrizations of Plane Curves The coordinates.

Slides:



Advertisements
Similar presentations
Precalculus 2 Section 10.6 Parametric Equations
Advertisements

A set of ordered pairs is called a __________.
Copyright © Cengage Learning. All rights reserved.
© 2010 Pearson Education, Inc. All rights reserved.
PARAMETRIC EQUATIONS AND POLAR COORDINATES 9. Usually, we use Cartesian coordinates, which are directed distances from two perpendicular axes. Here, we.
9.1 Parametric Curves 9.2 Calculus with Parametric Curves.
MAT 171 Precalculus Algebra Section 9-7 Parametric Equations Cape Fear Community College Dr. Claude S. Moore.
Relations The key question: How is a relation different from a function?  A relation is a set of ordered pairs (x, y) of real numbers.  The graph of.
 We can define both elements of the ordered pair, (x, y), in terms of another variable, t, called a parameter.  Example: Given and, a) Find the points.
Learning Targets Define parametric equations Graph curves parametrically within a given parametric interval Eliminate the parameter to obtain a rectangular.
Assigned work: pg. 433 #1-12 Equation of a line – slope and point or two points BUT NOW we will learn to describe an Equation of a Line by using vectors…………………..
Calculus and Analytic Geometry II Cloud County Community College Spring, 2011 Instructor: Timothy L. Warkentin.
1.4 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for.
10.2 – 10.3 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations.
Chapter 10 – Parametric Equations & Polar Coordinates 10.1 Curves Defined by Parametric Equations 1Erickson.
PARAMETRIC FUNCTIONS Today we will learn about parametric functions in the plane and analyze them using derivatives and integrals.
1.4 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for.
Copyright © Cengage Learning. All rights reserved. 9 Topics in Analytic Geometry.
Plane Curves and Parametric Equations New Ways to Describe Curves (10.4)
Section 11.1 Plane Curves and Parametric Equations By Kayla Montgomery and Rosanny Reyes.
1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Greg Kelly, 2005 Mt. Washington Cog Railway, NH.
10.6 Plane Curves and Parametric Equations. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection.
Copyright © 2011 Pearson, Inc. 6.3 Parametric Equations and Motion.
Review: 1. Solve for a: 4 3 = 2 a 2. What is the domain for y = 2e -x - 3? 3. What is the range for y = tan x?
1.4 Parametric Equations. Relations Circles Ellipses Lines and Other Curves What you’ll learn about… …and why Parametric equations can be used to obtain.
Sullivan Algebra and Trigonometry: Section 11.7 Objectives of this Section Graph Parametric Equations Find a Rectangular Equation for a Curve Defined Parametrically.
12.1 Parametric Equations Math 6B Calculus II. Parametrizations and Plane Curves  Path traced by a particle moving alone the xy plane. Sometimes the.
P ARAMETRIC E QUATIONS Section Plane Curves and Parametric Equations Consider the path of an object that is propelled into air at an angle of 45°.
Parametric Surfaces and their Area Part II. Parametric Surfaces – Tangent Plane The line u = u 0 is mapped to the gridline C 2 =r(u 0,v) Consider the.
Warm-Up 1/ C Assignments Questions? H.
9.5. If f and g are continuous functions of t on an interval I, the set of ordered pairs (f(t), g(t)) is a plane curve, C. The equations given by x =
Parametric Equations. In a rectangular coordinate system, you will recall, a point in the plane is represented by an ordered pair of number (x,y), where.
Parametric Equations Greg Kelly, Hanford High School, Richland, Washington.
2.1 “Relations & Functions” Relation: a set of ordered pairs. Function: a relation where the domain (“x” value) does NOT repeat. Domain: “x” values Range:
Precalculus Parametric Equations graphs. Parametric Equations  Graph parametric equations.  Determine an equivalent rectangular equation for parametric.
Prerequisites for Calculus
Parametric Surfaces and their Area Part I
Section 6.3: Arc Length Practice HW from Stewart Textbook (not to hand in) p. 465 # 1-13 odd.
Semester 1 Final Review D Plot the point (4, -2) in the coordinate plane. (Lesson 4.1) Name the quadrant the point is in.
Homework Questions…. Pre-Calculus Section 6.3 in your book…
Parametric Equations Until now, we’ve been using x and y as variables. With parametric equations, they now become FUNCTIONS of a variable t.
The point P belongs to the plane π if the vector Vector is coplanar with the vectors and Vector Equation of the Plane.
Parametric equations Parametric equation: x and y expressed in terms of a parameter t, for example, A curve can be described by parametric equations x=x(t),
Bell Ringer Solve even #’s Pg. 34.
3.1 Functions x is called the independent variable
Linear Inequalities Solution to inequality in one variable – interval on number line Solution to inequality in two variables – points in the plane Graph.
8.7Systems of Linear Equations – Part 1
© 2010 Pearson Education, Inc. All rights reserved
Date Calculus AB Ms. Brewer
Parametric Equations and Polar Coordinates
ALGEBRA II HONORS/GIFTED - SECTION 2-8 (Two-Variable Inequalities)
Start Up Day 51.
Parametric Equations Accelerated Math 3.
Plane Curves & Parametric Equations (10.2)
11.7 Circles in the Coordinate Plane
x = 4y - 4 x = 4y + 4 x = 4y - 1 y = 4x - 4 y = 4x - 1 y = 4x + 4
Parametric Equations & Plane Curves
1.4 Parametric Equations Mt. Washington Cog Railway, NH.
Section 6.3 Parametric Equations
1.4 Parametric Equations Mt. Washington Cog Railway, NH
Parametric equations Problem solving.
Parametric Equations and Motion
8.6 – Parametric Equations and Graphs
9.5 Parametric Equations.
1.4 Parametric Equations Mt. Washington Cog Railway, NH
Graph lines given their equation. Write equations of lines.
3.6 Parallel Lines in the Coordinate Plane
Prerequisites for Calculus
and Parametric Equations
Graphing Systems of Equations.
Presentation transcript:

Parametric Equations: another process to describe a plane curve on the Cartesian coordinate system – Parametrizations of Plane Curves The coordinates (x and y) are described by the same auxiliary variable called the parameter (t). There are different parameterizations that produce the same graph or curve. Parametric equations are continuous on an interval. The parameter (t) usually represent time. As it increases, it gives direction to the curve.

11.1 – Parametrizations of Plane Curves Simple curve – distinct values of the parameter yield distinct points. No overlapping occurs. Closed curve – initial and final values of the parameter on an interval yield the same point. A simple curve can be drawn without lifting the pencil from the paper, and without passing through any point twice. A closed curve has the same starting and ending points, and is also drawn without lifting the pencil from the paper. Simple; closed Simple; not closed Not simple; closed Not simple; not closed

11.1 – Parametrizations of Plane Curves