Calc01_4 - → 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

1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, Washington

This preview has intentionally blurred sections. Sign up to view the full version.

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) →

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 →

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

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 →

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document