L30 Parametric Equations - amples 4 5 x = cos 2 t y = sin 2 t \u00b1 t \u00b1 2 \u00b1 What\u2019s the di\u00b1erence between(3 and(5 5 6 x = sin t y = sin 2 t \u00b1 t \u00b1 2

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

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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
2. x ( t ) = 1 + 3 t; y ( t ) = 2 ± t 2 2
3. x = cos t; y = sin t; 0 ± t ± 2 ± 3
4. x = sin t; y = cos t; 0 ± t ± ± What’s the di±erence between the last two ex-

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