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...

• 10

This preview shows page 1 - 7 out of 10 pages.

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.