This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 1432 Notes – Session 4 9.6 Parametric Curves Let ) ( t x and ) ( t y be functions where t is the parameter. ( 29 ) ( ), ( t y t x is the point that traces out the curve. Example 1: Express the curve by an equation in x and y; then pl ot : ( 29 ∞ ∞ ∈ = = , 2 5 ) ( 1 3 ) ( t t t y t t x Example 2: Express the curve by an equation in x and y: 2 2 ) ( ) ( ≤ ≤ + + + = = t e t y e t x t t If t is restricted to lie on an interval [ a, b ] then x(t) and y(t) would have an initial point ( x(a), y(a)) and a terminal point (x(b), y(b)) . So a parametric curve has an orientation given by the parameterized variable. Example 3: Express the curve by an equation in x and y: π ≤ ≤ = = t t t y t t x cos 2 ) ( cos 3 ) ( Example 4: Express the curve by an equation in x and y ( ) cos ( ) 2 sin 2 x t t y t t t π = = ≤ ≤ Example 5: Express the curve by an equation in x and y; then pl ot t t y t t x tan ) ( sec ) ( = = To parameterize a line SEGMENT from ( 29 , y x to ( 29 1 1 , y x : 1 ) ( ) ( ) ( ) ( 1 1 ≤...
View
Full
Document
This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.
 Summer '10
 JEFFMORGAN

Click to edit the document details