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# Calc01_4 - ≥ 2 y x = x ≥ parabolic function → t...

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1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, Washington Photo by Greg Kelly, 2005 Mt. Washington Cog Railway, NH

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There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for the x and y coordinates in terms of a third variable (usually t or ). x f t y g t These are called parametric equations. t ” is the parameter. (It is also the independent variable)
Example 1: 0 x t y t t To graph on the TI-89: MODE Graph……. 2 ENTER PARAMETRIC Y= xt1 t yt1 t 2nd T ) ENTER WINDOW GRAPH

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Hit zoom square to see the correct, undistorted curve. We can confirm this algebraically: x t y t x y 2 x y 0 x 2 y x 0 x

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Unformatted text preview: ≥ 2 y x = x ≥ parabolic function → t Circle: If we let t = the angle, then: cos sin 2 x t y t t π = = ≤ ≤ Since: 2 2 sin cos 1 t t + = 2 2 1 y x + = 2 2 1 x y + = We could identify the parametric equations as a circle. → Graph on your calculator: Y= xt1 cos( ) t = yt1 sin( ) t = WINDOW GRAPH 2 π Use a [-4,4] x [-2,2] window. → Ellipse: 3cos 4sin x t y t = = cos sin 3 4 x y t t = = 2 2 2 2 cos sin 3 4 x y t t + = + 2 2 1 3 4 x y + = This is the equation of an ellipse. π...
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