sn4_1 - Math 1432 Notes Session 4 9.6 Parametric Curves Let...

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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: - = = 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 = = 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...
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sn4_1 - Math 1432 Notes Session 4 9.6 Parametric Curves Let...

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