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University of Massachusetts, Lowell *

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2310

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Chemistry

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Oct 30, 2023

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pdf

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11

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Quiz 2 13.3 13 41 Friday Ch 13 Practice Problems s questions added offine Hours Friday 3 40 4 40pm Olsen 404 or 406 201 Parametric Equations There are some limitations of our tradional definition of function Suppose we wanted to model the motion of a particle at time t É Éa function difficult to describe in a single closed equation does not show a direction Solution If we define x Ely El later z in terms of new independent variable often we use t or s we can get around this t it y h t we call this new variable a parameter In general parametric curves consist of all points in a plane Cor in space which satisfy x y gct h t where tE a b Note while t usually means time it can mean any arbitrary parameter
ext Graph Analyze the parametric equation X ZE y t 2 For EE 0,3 one way to graph is to make a table 1 2 3 2,3 2 4 6 4,61 3 6 11 4111 drawn with positive orientation w yj i
Eliminatingthefarameter To make graphing easier we can sometimes eliminate parameter using algebra or trigonometry titties sometimes this can be difficult or impossible we can lose direction From above example eliminate E x L t y 2 for EE 0,3 solve one equation for t 4 E substitute into other equation y E 2 2 Find limitations on x OLE E3 y FWÉxE 06 0 2243 02 16 Ez Eliminate parameter describe graph a x 310s II y 35in TE on tE 0,4 T.tn teIgmt Eeintities scosotsin 0 1 square both sides of both equations Cios E yEGsin E
x 910s TE y 2 9 sin It Add two equations together x y 9 cos at 9 sin TE 2 5 9 EL t l xty circle of radius 3 centered at CAREFUI teco 4 x 3 Ig y 3sin th plugging in values of ti 0 ft x 3cos E x 3 105207 3 3 1051T 3 9 3 sin 107 0 p qy yes no y o 4 Chek 4 2 Cos Hz O y 35in H2 3
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