Calc01_4.ppt - 1.4 Parametric Equations Mt Washington Cog Railway NH Photo by Greg Kelly 2005 Greg Kelly Hanford High School Richland Washington There

Calc01_4.ppt - 1.4 Parametric Equations Mt Washington Cog...

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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
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
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
t Circle: If we let t = the angle, then: cos sin 0 2 x t y t t   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 Use a [-4,4] x [-2,2] window.

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