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

-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.