1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Greg Kelly,...
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Transcript of 1.4 Parametric Equations Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Greg Kelly,...
1.4 Parametric Equations
Greg Kelly, Hanford High School, Richland, WashingtonPhoto 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 calledparametric equations.
“t” is the parameter. (It is also the independent variable)
Example 1: 0x t y t t
To graph on the TI-89:
MODE Graph……. 2 ENTER
PARAMETRIC
Y= xt1 t
yt1 t2nd T ) ENTER
WINDOW
GRAPH
Hit zoom square to see the correct, undistorted curve.
We can confirm this algebraically:
x t y t
x y
2x y 0x
2y x 0x
parabolic function
t
Circle:
If we let t = the angle, then:
cos sin 0 2x t y t t
Since: 2 2sin cos 1t t
2 2 1y x
2 2 1x y We could identify the parametric equations as a circle.
Graph on your calculator:
Y=
xt1 cos( )tyt1 sin( )t
WINDOW
GRAPH
2
Use a [-4,4] x [-2,2] window.
Ellipse: 3cos 4sinx t y t
cos sin3 4
x yt t
2 22 2cos sin
3 4
x yt t
2 2
13 4
x y
This is the equation of an ellipse.