PolarGraph1

Graphing a Parametric or Polar Curve

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This PG code shows how to graph a parametric curve or polar curve with a shading (a filled region).

• File location in OPL: FortLewis/Authoring/Templates/Parametric/PolarGraph1.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGgraphmacros.pl", "AnswerFormatHelp.pl", "unionTables.pl", ); TEXT(beginproblem()); $refreshCachedImages = 1;	Initialization: We use PGgraphmacros.pl to generate the graph, and unionTables.pl to put the text and the graph side-by-side. We should set $refreshCachedImages = 1; so that changes in the graph will show up (not get stuck by old images in the browser cache).
Context("Numeric")->variables->are(t=>"Real"); $gr = init_graph(-1.1,-1.1,1.1,1.1,axes=>[0,0],size=>[300,300]); # # Define some useful colors # $gr->new_color("lightblue", 198,217,253); # RGB $gr->new_color("darkblue", 77,137,249); $gr->new_color("lightred", 255,127,127); $gr->new_color("darkred", 255, 55, 55); $gr->new_color("lightorange", 255,204,127); $gr->new_color("darkorange", 255, 153, 0); $gr->new_color("lightgreen", 187, 255, 153); $gr->new_color("darkgreen", 0, 208, 0); # # For a polar curve r = f(t), # x = r cos(t) = f(t) cos(t) # y = r sin(t) = f(t) sin(t) # $x = Formula("cos(5*t) * cos(t)"); $y = Formula("cos(5*t) * sin(t)"); $f = new Fun( $x->perlFunction, $y->perlFunction, $gr ); $f->domain(0,3.14); $f->steps(90); $f->weight(2); $f->color('darkgreen'); $gr->fillRegion([0.5,0.1,'lightgreen']);	Setup: We initialize a graph object named $gr. We define several new named colors which you can use if you want. We construct MathObjects formulas $x and $y for the x- and y-coordinates in terms of the parameter t. Then, we pass these formulas to the Fun routine, converting them to perl subroutines via ->perlFunction, and attach them to the graph object $gr. Then, we set some of the options for the graph of the parametric curve $f. Finally, we fill the region enclosing the point (0.5,0.1) with the color light green.
Context()->texStrings; BEGIN_TEXT \{ ColumnTable( "Find the area enclosed by one petal of the rose curve \( r = f(\theta) = \cos(5\theta) \). $BR $BR Area = ". ans_rule(20).$SPACE. AnswerFormatHelp("numbers") , $BCENTER. image( insertGraph($gr), width=>300, height=>300 ). $PAR. "Graph of \( r = \cos(5\theta) \)". $ECENTER , indent => 0, separation => 30, valign => "TOP" ); \} END_TEXT Context()->normalStrings;	Main Text: We use the ColumnTable(column 1, column 2, options) to put the text and graph side-by-side. We join (Perl) strings " " to common PG commands like ans_rule(20) using the string concatenation operator . which is a period. Notice that the commas between column 1, column 2, and the options do not have any periods before them.
$showPartialCorrectAnswers = 1; # intentionally incorrect ANS( Compute("pi")->cmp() );	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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