L30 Parametric Equations

L30 Parametric Equations - amples? 4 5. x = cos 2 t; y =...

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Lecture 30: Parametric Equations Def. Suppose x and y are both given as func- tions of a third variable t (called a parameter ) by the parametric equations x = f ( t ) ; y = g ( t ). Each value of t determines a point ( x;y ), which we can plot in a coordinate plane. As t varies, the point ( x;y ) = ( f ( t ) ;g ( t )) traces out a parametric curve. ex. Sketch the graph of the curve given by the parametric equations 1. x ( t ) = t; y ( t ) = t 2 ; 0 ± t ± 1. 1
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2. x ( t ) = 1 + 3 t; y ( t ) = 2 ± t 2 2
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3. x = cos t; y = sin t; 0 ± t ± 2 ± 3
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4. x = sin t; y = cos t; 0 ± t ± ± What’s the di±erence between the last two ex-
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Unformatted text preview: amples? 4 5. x = cos 2 t; y = sin 2 t; t 2 Whats the dierence between (3) and (5)? 5 6. x = sin t; y = sin 2 t; t 2 6 NYTI: 1. x = e 2 t ; y = t + 1 ; 2. x = 5 cos t +2 ; y = 3 sin t 1 ; t 2 3. x = 1 + 2 e t ;y = 3 e t Tonights homework: Work out the NYTI prob-lems above. 7...
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This note was uploaded on 02/14/2012 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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L30 Parametric Equations - amples? 4 5. x = cos 2 t; y =...

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