WOLFRAM|DEMONSTRATIONS PROJECT

Plotting Vector-Valued Functions

​
t
0.01
​
​
x(t) =
acos(t)
cos(at)
a
2
cos
(t)
asin(t)
cos(at)

a
-2
-1
1
2
y(t) =
bsin(t)
sin(bt)
1-bsin(t)
bt
sin(at)

b
-2
-1
1
2
z(t) =
bt
b
2
t
ct

3
cx
xsin(x)
c
c
-2
-1
1
2
One way to represent a vector-valued function is to graph the parametric plot for
x(t)
,
y(t)
on the
x
y
plane, the parametric plot for
x(t)
,
z(t)
on the
x
z
plane, and the parametric plot for
y(t)
,
z(t)
on the
y
z
plane. The graph of the vector-valued function
{x(t),y(t),z(t)}
then shows each of these parametric plots as their orthogonal projections onto each of the coordinate planes.