(*^
::[ Information =
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*)
Needs["Graphics`Graphics`"]
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(*
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POLAR GRAPHING
:[font = text; inactive; preserveAspect]
The object of this lesson is to teach students to analyze
basic polar graphs through experimentation with
computer graphing.
;[s]
1:0,1;126,-1;
2:0,26,19,Calculus,0,12,0,0,0;1,26,19,Calculus,0,12,21845,21845,21845;
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;[s]
1:0,1;2,-1;
2:0,12,10,Courier,1,12,0,0,0;1,23,16,CalcMath,1,12,21845,21845,21845;
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:[font = text; inactive; preserveAspect]
This lesson will be looking at polar equations
in the form Sin[a theta]. Place the mouse on
the cell , click once, and push enter to see a display of five graphs of equations in this form.
;[s]
3:0,1;65,2;82,1;201,-1;
3:0,26,19,Calculus,0,12,0,0,0;2,26,19,Calculus,0,12,0,0,65535;1,26,19,Calculus,0,12,65535,0,0;
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--
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Clear[a,theta,lplot,pplot,t]
Do[
lplot := Graphics[Text[Sin[a theta],
{Cos[((.5 a a-5.5 a +17) (Pi/32)+.72)],
Sin[(.5 a a-5.5 a +17) Pi/32]}]];
pplot := PolarPlot[Sin[a theta],{theta,0,2Pi},
PlotRange->{{-1,1},{-1,1}},
PlotStyle->RGBColor[a/5.01,1-a/5.01,0],
DisplayFunction->Identity];
Show[pplot,lplot,DisplayFunction->$DisplayFunction]
,{a,1,5}]
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When you reach this spot, return to the first graph displayed,
group the cells--one click on second cell grouping --
and push command Y to see an animated display of all
five graphs. Notice simiarities and differences in the graphs
as the value of a changes. You will want to see more
graphs of this type before you sketch the graphs on your worksheet;use the computer to graph equations by typing in the following:
PolarPlot [Sin[(insert number) theta],{theta,0,nPi}]
IMPORTANT: n must be chosen so that the graph
displayed runs from -1 to 1 on the horizontal axis.
;[s]
7:0,0;130,1;142,0;258,2;261,0;503,3;618,0;629,-1;
4:4,26,19,Calculus,0,12,0,0,65535;1,26,19,Calculus,1,12,0,0,65535;1,28,20,Calculus,8,12,0,0,65535;1,26,19,Calculus,2,12,0,0,65535;
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Now, I hope that you were curious enough to try many different
numbers -- the world does not live by whole numbers alone!
If you didn't try a variety of numbers, do so now -- I did
while working late one night on the worksheet. Remember that
with the aid of the computer, you can explore more than ever
before.
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Now that you can quickly sketch equations in the form of
Sin[ a theta],
let's change the form to Cos[a theta].
Get started! You know what to do.
;[s]
5:0,0;75,2;90,0;120,1;134,0;184,-1;
3:3,26,19,Calculus,0,12,0,0,65535;1,26,19,Calculus,0,12,65535,0,0;1,26,19,Calculus,0,12,65535,0,65535;
^*)