View of /trunk/NationalProblemLibrary/Rochester/setVectors5Coordinates/urvc_3_3.pg

    1 ## DESCRIPTION
    2 ##   Rectangular to Cylindrical Coordinates
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Coordinate', 'Rectangular', 'Cylindrical')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('Cylindrical and Spherical Coordinates')
   11 ## Date('5/30/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a1 = random(-5,-1,1);
   34 $b1 = random(1,5,1);
   35 $c1 = random(-5,5,1);
   36 $pi = arccos(-1);
   37 
   38 BEGIN_TEXT
   39 $PAR
   40  What are the cylindrical coordinates of the point whose rectangular coordinates
   41  are \( (x= $a1 ,\  y= $b1 ,\ z= $c1 ) \) ?
   42 $PAR
   43 $BR
   44 \( r \) = \{ans_rule(20)\} $BR
   45 \( \theta \) = \{ans_rule(20)\} $BR
   46 \( z \) = \{ans_rule(20)\} $BR
   47 END_TEXT
   48 
   49 
   50 $ans0 =  ($a1*$a1+$b1*$b1)**.5 ;
   51 $ans1 =  arctan($b1/$a1)+$pi ;
   52 $ans2 =  $c1 ;
   53 
   54 
   55 ANS(num_cmp($ans0));
   56 ANS(num_cmp($ans1));
   57 ANS(num_cmp($ans2));
   58 
   59 ENDDOCUMENT();        # This should be the last executable line in the problem.