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

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Math 1432 Notes – Session 4 9.6 Parametric Curves Let ) ( t x and ) ( t y be functions where t is the parameter. ( ) ( ), ( 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 : ( - - = - = , 2 5 ) ( 1 3 ) ( t t t y t t x Example 2: Express the curve by an equation in x and y: 2 0 2 ) ( ) ( + + + = = - t e t y e t x t t
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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 0 cos 2 ) ( cos 3 ) ( Example 4: Express the curve by an equation in x and y ( ) cos ( ) 2sin 0 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 ) ( = =
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To parameterize a line SEGMENT from ( 0 0 , y x to ( 1 1 , y x : 1 0 ) ( ) ( ) ( ) ( 0 1 0 0 1 0 - + = - = t y y t y t y x x t x t x For a LINE: - t Example 6: Parameterize the line segment from (4, 6) to (-1, 3)
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You try! (hw9 #1, 2 and 9)
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