https://courses1.webwork.maa.org:8080/wwtmp/ElizabethtownC-MA122/gif/gabriela_sanchis-1125-set10_3_Polar_Coordinates-prob8--https://courses1.webwork.maa.org:8080/wwtmp/ElizabethtownC-MA122/gif/gabriela-Q-sanchis-3828-set10-Q-3_Polar_Coordinatesprob8image1.png
but it should be just the last part: https://courses1.webwork.maa.org:8080/wwtmp/ElizabethtownC-MA122/gif/gabriela-Q-sanchis-3828-set10-Q-3_Polar_Coordinatesprob8image1.png
Here is my code. Thanks in advance for any help.
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"PGunion.pl",
"imageChoice.pl",
);
TEXT(beginproblem());
$refreshCachedImages = 1;
##############################################################
#
# Setup
#
#
Context("Numeric")->variables->are(t=>"Real",x=>"Real");
$a=random(1,5);
$b1=random(1,5);
$b=$a+$b1;
$c=random(1,5);
$d=1.1*($a+$b);
$lb="\(2\pi\)";
for ($i=0; $i<=7; $i++) {$gr[$i] = init_graph(-$d,-$d,$d,$d,axes=>[0,0],size=>[300,300]);$gr[$i]->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)
#
$x[0] = Formula("($b-$a*cos($c*t)) * cos(t)");
$y[0] = Formula("($b-$a*cos($c*t))* sin(t)");
$g[0]=Formula("$b-$a*cos($c*x)");
$x[1] = Formula("($b+$a*cos($c*t)) * cos(t)");
$y[1] = Formula("($b+$a*cos($c*t))* sin(t)");
$g[1]=Formula("$b+$a*cos($c*x)");
#$x[0] = Formula("($a-$b*cos($c*t)) * cos(t)");
#$y[0] = Formula("($a-$b*cos($c*t))* sin(t)");
#$g[0]=Formula("$a-$b*cos($c*x)");
#$x[1] = Formula("($a+$b*cos($c*t)) * cos(t)");
#$y[1] = Formula("($a+$b*cos($c*t))* sin(t)");
#$g[1]=Formula("$a+$b*cos($c*x)");
$x[2] = Formula("($b-$a*sin($c*t)) * cos(t)");
$y[2] = Formula("($b-$a*sin($c*t))* sin(t)");
$g[2]=Formula("$b-$a*sin($c*x)");
$x[3] = Formula("($b+$a*sin($c*t)) * cos(t)");
$y[3] = Formula("($b+$a*sin($c*t))* sin(t)");
$g[3]=Formula("$b+$a*sin($c*x)");
#$x[2] = Formula("($a-$b*sin($c*t)) * cos(t)");
#$y[2] = Formula("($a-$b*sin($c*t))* sin(t)");
#$g[2]=Formula("$a-$b*sin($c*x)");
#$x[3] = Formula("($a+$b*sin($c*t)) * cos(t)");
#$y[3] = Formula("($a+$b*sin($c*t))* sin(t)");
#$g[3]=Formula("$a+$b*sin($c*x)");
for ($i=0; $i<=3; $i++) {$gr1[$i] = init_graph(-1,-$d,7.28,$d,axes=>[0,0],size=>[300,300]);
$gr1[$i]->new_color("darkred", 255, 55, 55);
add_functions($gr1[$i], "$g[$i] for x in <0,6.28>" . " using color:darkred and weight:2");
$gr1[$i]->h_ticks(0,"black",1.57,3.14,4.71,6.28);
$gr1[$i]->v_ticks(0,"black",1);
$gr1[$i]->lb( new Label(6.28,-.5,'2pi',
'black','center','middle'));
};
for ($i=0; $i<=3; $i++) {$f = new Fun( $x[$i]->perlFunction, $y[$i]->perlFunction, $gr[$i] );
$f->domain(0,6.28);
$f->steps(180);
$f->weight(2);
$f->color('darkgreen');
};
foreach $j (0..3) {
$fig[$j] = image(insertGraph($gr1[$j]),
width => 300, height => 300, tex_size => 310);
}
@QA = ();
foreach my $i (0..3) { push( @QA, "$fig[$i]", $gr[$i] ); }
$ml = new_image_match_list(
link => 1, # do not link to separate image
size => [300,300], # image size in pixels
tex_size => 450, # tex size in precent times 10
columns => 1, # number of columns
separation => 20, # separation between image columns
);
$ml->rf_print_q(~~&pop_up_list_print_q); # use pop-up-lists
$ml->ra_pop_up_list([ No_answer=>"?", A=>"A", B=>"B", C=>"C", D=>"D"] );
$ml->qa(@QA); # set the questions and answers
$ml->choose(4); # select 4 of them
#$ml->choose_extra(0); # and show the other 1##############################################################
#
# Text
#
#
Context()->texStrings;
BEGIN_TEXT
The figures on the left show graphs of \(r\) as a function of \(\theta\) in Cartesian coordinates, where \(0\leq\theta\leq2\pi\). Match each with the corresponding polar curve shown on the right.
$PAR
\{
ColumnTable(
$ml->print_q() # no period!
, # comma!
$BCENTER.
$ml->print_a().
$BR.
$ECENTER # no period!
, # comma!
indent => 0, separation => 30, valign => "TOP"
)
\}
END_TEXT
Context()->normalStrings;
##############################################################
#
# Answers
#
#
install_problem_grader(~~&std_problem_grader);
$showPartialCorrectAnswers = 0;
ANS(str_cmp($ml->ra_correct_ans));
foreach my $i (0..3) {
$a[$i] = $ml->ra_correct_ans->[$i];
}
ENDDOCUMENT();