PPP Lesson 1.4
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Transcript PPP Lesson 1.4
1.4 Parametric Equations
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:
x t
y t
t 0
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
y x2
x y
x2 y
x0
x0
parabolic function
Circle:
If we let t = the angle, then:
t
x cos t
Since:
y sin t
0 t 2
sin 2 t cos 2 t 1
y 2 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 )
2
Use a [-4,4] x [-2,2]
window.
WINDOW
GRAPH
Ellipse:
x 3cos t
y 4sin t
x
cos t
3
y
sin t
4
2
2
x y
2
2
cos
t
sin
t
3 4
2
2
x y
1
3 4
This is the equation
of an ellipse.