WOLFRAM|DEMONSTRATIONS PROJECT

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.