## DESCRIPTION
## Parametric equations: graphing a polar curve
## ENDDESCRIPTION

## KEYWORDS('parametric', 'graph polar curve')

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('Fort Lewis Tutorial 2011')
## Date('01/30/2011')
## Author('Paul Pearson')
## Institution('Fort Lewis College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


###########################
#  Initialization

DOCUMENT();      

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"AnswerFormatHelp.pl",
"unionTables.pl",
);

TEXT(beginproblem());

$refreshCachedImages = 1;


##########################
#  Setup

Context("Numeric")->variables->are(t=>"Real");

$gr = init_graph(-1.1,-1.1,1.1,1.1,axes=>[0,0],size=>[300,300]);


$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);

#  If the polar curve is r = f(t) = cos(5*t), then
#
#  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->color('darkgreen');
$f->weight('2');

$gr->fillRegion([0.5,0.1,'lightgreen']);


##########################
#  Main Text 

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;


########################
#  Answer Evaluation

$showPartialCorrectAnswers = 1;

# intentionally incorrect
ANS( Compute("pi")->cmp() );


############################
#  Solution

Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();