1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, Washington 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: x t y t t0 To graph on the TI-89: MODE Graph……. 2 PARAMETRIC ENTER 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 x2 y y x2 x0 x0 parabolic function Circle: If we let t = the angle, then: t x cos t y sin t 0 t 2 Since: sin 2 t cos2 t 1 y2 x2 1 We could identify the parametric equations as a circle. x2 y 2 1 Graph on your calculator: Y= xt1 cos(t) yt1 sin(t) Use a [-4,4] x [-2,2] window. WINDOW GRAPH 2 Ellipse: x 3cos t y 4sin t x cos t 3 2 2 y sin t 4 x y cos2 t sin 2 t 3 4 x y 1 3 4 2 2 This is the equation of an ellipse.
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