Choose XRng, YRng &
θ
Rng
θ
Step and smoothness
Changing the default for
θ
Step
Circular circles
13
T
T
H
H
E
E
P
P
O
O
L
L
A
A
R
R
A
A
P
P
L
L
E
E
T
T
This aplet is used to graph functions of the type where the radius r is a function of the angle
θ
(theta). As with
the Parametric aplet, it is very similar to the Function aplet and so the space devoted to it here is limited
mainly to the way it differs. Some examples of functions of this type, together with their graphs are:
R
1(
θ
)
=
4 cos(3
θ
)
R
2(
θ
)
=
0.5
θ
R
3(
θ
)
= +
3 2 sin(10
θ
)
The
PLOT SETUP
view shows that ranges must be specified not only for
X
and
Y
but for
θ
. The values set for
XRng
and
YRng
control the length
of the axes. The movement of the cursor follows the increments set for
θ
in
θ
Step
regardless of the resulting
X
and
Y
positions.
The values of
θ
Rng
and for
θ
Step
are critical in controlling the appearance of the graph. The values set for
θ
Rng
control how much of the graph is drawn, while the values for
XRng
and
YRng
only control how much
of the graph is displayed on the screen once drawn.
θ
Step
controls how smooth the graph is, as did
TStep
in the Parametric aplet. The default values for
θ
Rng
are
0
≤
θ ≤
2
π
and the default value for
θ
Step
is
π
/
24
.
The default for
θ
Step
often results in graphs which are not very smooth and 0.05 is a better compromise
between smoothness & speed. If you particularly want to use a fraction of
π
to aid in tracing the graph then
π
try /
60
.
If it is important that graphs of circles do not look oval, then use the
default values for the axes. If the resulting axes don’t show enough of
the function, then
in or out. The
Square
option can also
be used to achieve round circles.
98
