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T
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H
H
E
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P
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O
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L
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A
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R
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A
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P
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T
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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:
1( )
4 cos(3 )
R
θ
θ
=
2( )
0.5
R
θ
θ
=
3( )
3
2 sin(10 )
R
θ
θ
= +
Choose XRng, YRng &
θ
Rng
The
PLOT
SETUP
view shows that ranges must
be specified not only for X and Y but for
θ
. The
values set for XRange and YRange 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.
θ
Step and smoothness
The values of
θ
Range and for
θ
Step are critical in controlling the appearance
of the graph. The values set for
θ
Range control how much of the graph is
drawn, while the values for XRange and YRange 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
Range are
0
2
θ
π
≤ ≤
and the default value for
θ
Step is
π
/
24
.
Changing the default for
θ
Step
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 try
π
/
60
.
Circular circles
If it is important to have a set of axes that are
‘square’, so that circles do not look oval, then
use the default values. 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.
