12
T
T
H
H
E
E
E
E
X
X
P
P
E
E
R
R
T
T
:
:
V
V
E
E
C
C
T
T
O
O
R
R
F
F
U
U
N
N
C
C
T
T
I
I
O
O
N
N
S
S
F
F
u
u
n
n
a
a
n
n
d
d
g
g
a
a
m
m
e
e
s
s
Apart from the normal mathematical and engineering applications of parametric equations, some interesting
graphs are available through this aplet. Three quick examples are given below.
Example 1
Try exploring variants of the graph of:
( )
=
3sin 3
t
x t
( )
=
2sin 4
t
y t
Example 2
Try varying the values of
A
and
B
in the equations:
+
)
−
x
1(
t
)
=
(
A B
)cos(
t
B
cos((
A
t
B
+
1) )
1(
+
)
−
y t
)
=
(
A B
)sin(
t
B
sin((
A
t
B
+
1) )
Hint:
An easy way to vary A and B is to store values to memories
A
and
B
in the
HOME
view and enter the
equations exactly as shown. New graphs can then be created by changing back to
HOME
and
storing different values to
A
and
B
. The example shown uses
A=4
,
B=2.5
and has axes set with
TRng
of 0 to 31.5 step .2,
XRng
of -21.66 to 21.66 and
YRng
of -12 to 9. It also has
Axes
un-
’d in
PLOT SETUP.
Example 2
Try varying the constants in the equations:
x
1(
t
)
=
3sin(
t
)
+
2sin(15
t
)
1(
y t
)
=
3cos(
t
)
+
2cos(15
t
)
For those who remember them, this is curve like those produced by a “Spirograph”.
95
