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Parametric Plots from Rectangular Plots

​
t
0.01
​
​
x(t) =
acos(t)
cos(at)
a
2
cos
(t)
asin(t)
cos(at)
e
a
-2
-1
1
2
y(t) =
bsin(t)
sin(bt)
1-bsin(t)
bt
sin(bt)
e
b
-2
-1
1
2
Equations for
x(t)
and
y(t)
are plotted on the perpendicular
x,t
and
y,t
planes as
t
varies from
-2π
to
2π
. The functions
x(t)
and
y(t)
can serve as a parametric representation for a function
y(x)
, which is plotted in purple on the
x
,
y
plane cutting
t=-2π
, shown in light gray.
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