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    1 ## DESCRIPTION
    2 ## Calculus: Polar Coordinates
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('polar coordinates')
    6 ## Tagged by jjh2b
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Parametric Equations and Polar Coordinates')
   10 ## DBsection('Curves Defined by Parametric Equations')
   11 ## Date('6/9/2006')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1(' ')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('11.1')
   23 ## Problem2('31')
   24 
   25 DOCUMENT();
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 1;
   37 
   38 $a = random(2,5);
   39 $c = random(1,4);
   40 $b = $a + $c;
   41 
   42 $funct = "-$b * sin (t)";
   43 
   44 BEGIN_TEXT
   45 The ellipse
   46  \[ \frac{x^2}{$a^2} + \frac{y^2}{$b^2} = 1 \]
   47 
   48 can be drawn with parametric equations. Assume the curve is traced
   49 clockwise as the parameter increases.
   50 $PAR
   51 If \( x = $a \cos(t)  \)
   52 $BR$BR
   53 then \(y\) =  \{ ans_rule(50) \}
   54 END_TEXT
   55 
   56 ANS(fun_cmp($funct, var=>'t', limits=>[[0, 6.283]]));
   57 
   58 ENDDOCUMENT();