Calc01_4 - → t Circle If we let t = the angle then cos...

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1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, Washington
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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 ). θ ( 29 x f t = ( 29 y g t = These are called parametric equations. t ” is the parameter. (It is also the independent variable)
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Example 1: 0 x t y t t = = To graph on the TI-89: MODE Graph……. 2 ENTER PARAMETRIC Y= ( 29 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 parabolic function
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Unformatted text preview: → 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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