1_Parametric - Parametric Equations To represent motion in...

Parametric Equations
To represent motion in the
xy
plane, let
x = f ( t )
describe the
horizontal motion and
y = g ( t )
describe the vertical motion.
x = f ( t )
y = g ( t )
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parametric equations of a curve with parameter t .
Cartesian equations only contain
x
and
y
terms such as
y = x
2
or x sin y + 3 y - x = 4
. Parametric equations enable us
to graph curves that are not functions.
ex.
x = sin(2 t ), y = cos(3 t ), 0 t 2 p

ex
.
x = - 2 + t , y = 3 + 2 t , - 3 t 3
ex.
x = - 2 +