Graph3DCylindrical1

Interactive Graphs of Functions in Cylindrical Coordinates

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This PG code shows how to make an interactive graph of a function in cylindrical coordinates that is displayed using the LiveGraphics3D Java applet.

• File location in OPL: FortLewis/Authoring/Templates/DiffCalcMV/Graph3DCylindrical1/Graph3DCylindrical1.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserVectorUtils.pl", "PGcourse.pl", "LiveGraphicsCylindricalPlot3D.pl", ); TEXT(beginproblem());	Initialization: We need to include the macros file LiveGraphicsCylindricalPlot3D.pl.
Context("Numeric"); Context()->variables->are(x=>"Real",y=>"Real",r=>"Real",t=>"Real"); $a = random(2,4,1); $plot = CylindricalPlot3D( function => Formula("$a*cos((r^2)/4)"), rvar => "r", tvar => "t", rmin => 0, rmax => 6, tmin => 0, tmax => 2*pi, rsamples => 20, tsamples => 15, axesframed => 1, xaxislabel => "X", yaxislabel => "Y", zaxislabel => "Z", outputtype => 4, );	Setup: We generate a string of plot data using CylindricalPlot3D(). Setting outputtype to something other than 4 will require you to read the source code of LiveGraphicsCylindricalPlot3D.pl and familiarize yourself with the details of the LiveGraphics3D java applet. For more information on how to work with the string of plot data, see Martin Kraus's LiveGraphics3D homepage, and the excellent article by Jonathan Rogness and Martin Kraus Constructing Mathlets Quickly Using LiveGraphics3D.
Context()->texStrings; BEGIN_TEXT \{ Live3Ddata( $plot, image => "bell-shape.png", size => [400,400], tex_size => 600, tex_center => 1, scale => 1.1, ); \} END_TEXT Context()->normalStrings;	Main Text: To display the string of plot data $plot, we use the Live3Ddata() routine provided by the macro LiveGraphics3D.pl, which is loaded automatically. After you construct the graph you like, don't forget to take a screen shot of it and make an image file such as bell-shape.png that will be used in the pdf hardcopy.
$showPartialCorrectAnswers = 1;	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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