View of /trunk/NationalProblemLibrary/Rochester/setPolarCoord1Points/ur_pc_1_2.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 
    6 ## KEYWORDS('Polar Coordinates')
    7 ## Tagged by tda2d
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Parametric Equations and Polar Coordinates')
   11 ## DBsection('Polar Coordinates')
   12 ## Date('')
   13 ## Author('')
   14 ## Institution('Rochester')
   15 ## TitleText1('')
   16 ## EditionText1('')
   17 ## AuthorText1('')
   18 ## Section1('')
   19 ## Problem1('')
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 0;
   33 $pi = 4*arctan(1);
   34 $r05 = non_zero_random(-4,4);
   35 $r1 = 2*$r05;                      #so r1,r2 r3 are even
   36 $r2 = $r1;
   37 $r3 = $r1;
   38 $r35 = non_zero_random(-4,4);
   39 $r4 = 2*$r35;                      #so r4 is even
   40 $r5 = $r1 + 3;                     #so r5 is odd
   41 $r55 = non_zero_random(-4,4);
   42 $r6 = 2*$r55;                      #so r6,r7 are even
   43 $r7 = $r2;
   44 
   45 $t1 = 1;
   46 $t15 = random(-3,3);
   47 $t2 = non_zero_random(-8,8,4) + 1;    #so t2 is odd (ne t1 mod4)
   48 $t3 = random(2,8) * random(-1,1,2);
   49 $t35 = non_zero_random(-4,3);
   50 $t4 = 3* $t35 + 1;                  #so t4 is 1 mod 3
   51 $t5 = 3* $t35 + 5;                  # so t5 is 2 mod 3
   52 $t55 = non_zero_random(-2,2);
   53 $t6 = 6*$t55 - 1;                   #so t6 is 5mod 6
   54 $t7 = 6*$t55 + 1;                   #so t7 is 1mod 6
   55 
   56 $x1 = ($r1) * cos ($t1 * $pi/4) /sqrt(2);
   57 $x2 = ($r2) * cos ($t2 * $pi/4) /sqrt(2);
   58 $x3 = ($r3) * cos ($t3 * $pi/2) ;
   59 if (abs($t3-int($t3/2)*2)>0) {$x3=0;} # if t3 is odd then x3=0
   60 $x4 = ($r4) * cos ($t4 * $pi/3) ;
   61 $x5 = ($r5) * cos ($t5 * $pi/3) ;
   62 $x6 = ($r6) * cos ($t6 * $pi/6) /sqrt(3) ;
   63 $x7 = ($r7) * cos ($t7 * $pi/6) /sqrt(3) ;
   64 
   65 $y1 = ($r1) * sin (($t1) * ($pi/4)) /sqrt(2) ;
   66 $y2 = ($r2) * sin (($t2) * ($pi/4)) /sqrt(2) ;
   67 $y3 = ($r3) * sin (($t3) * ($pi/2)) ;
   68 $y4 = ($r4) * sin (($t4) * ($pi/3)) /sqrt(3) ;
   69 $y5 = ($r5) * sin (($t5) * ($pi/3)) /sqrt(3) ;
   70 $y6 = ($r6) * sin (($t6) * ($pi/6)) ;
   71 $y7 = ($r7) * sin (($t7) * ($pi/6)) ;
   72 
   73 $questStr1 =EV2( " \(  ( $r1 , \frac{$t1 \pi}{4} ) \)");
   74 $ansStr1 = EV2(   '\( ( \{spf($x1, "%5.0f")\} \sqrt{2},
   75                         \{spf($y1,"%5.0f") \} \sqrt{2} ) \)');
   76 
   77 $questStr2 = EV2( " \(  ( $r2 , \frac{$t2 \pi}{4} ) \)");
   78 $ansStr2 = EV2(   '\( ( \{spf($x2, "%5.0f")\} \sqrt{2},
   79                         \{spf($y2,"%5.0f") \} \sqrt{2} ) \)');
   80 
   81 $questStr3 =EV2( " \(  ( $r3 , \frac{$t3 \pi}{2} ) \)");
   82 $ansStr3 = EV2(   '\( ( \{spf($x3, "%5.0f")\} , \{spf($y3,"%5.0f") \} ) \)');
   83 
   84 $questStr4 =EV2( " \(  ( $r4 , \frac{$t4 \pi}{3} ) \)");
   85 $ansStr4 = EV2(   '\( ( \{spf($x4, "%5.0f")\} , \{spf($y4,"%5.0f") \} \sqrt{3}) \)');
   86 
   87 $questStr5 =EV2( " \(  ( $r5 , \frac{$t5 \pi}{3} ) \)");
   88 $ansStr5 = EV2(   '\( ( \{spf($x5, "%5.1f")\} , \{spf($y5,"%5.1f") \} \sqrt{3}) \)');
   89 
   90 $questStr6 =EV2( " \(  ( $r6 , \frac{$t6 \pi}{6} ) \)");
   91 $ansStr6 = EV2(   '\( ( \{spf($x6, "%5.0f")\} \sqrt{3} ,
   92                         \{spf($y6,"%5.0f") \} ) \)');
   93 
   94 $questStr7 =EV2( " \(  ( $r7 , \frac{$t7 \pi}{6} ) \)");
   95 $ansStr7 = EV2(   '\( ( \{spf($x7, "%5.0f")\} \sqrt{3} ,
   96                         \{spf($y7,"%5.0f") \} ) \)');
   97 
   98 @questions =( $questStr1,$questStr2,$questStr3,$questStr4,$questStr5,$questStr6,$questStr7);
   99 @answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4, $ansStr5, $ansStr6, $ansStr7);
  100 
  101 # Now randomize the questions:
  102 @slice = &NchooseK(7,6);
  103 @shuffle = &shuffle(scalar(@slice));
  104 
  105 TEXT(EV2(<<EOT));
  106 For each set of Polar coordinates \( (r,\theta ) \),
  107 match the equivalent Cartesian coordinates \( (x,y) \).
  108 $BR
  109 Don't use a calculator. $BR
  110 EOT
  111 TEXT(
  112 &match_questions_list(@questions[@slice]),
  113 &OL(@answers[@slice[@shuffle]])
  114 );
  115 ANS(str_cmp( [ @ALPHABET[&invert(@shuffle)] ]  ) );
  116      ##the correct answers are obtained by applying
  117      ##the inverse (adjoint) permutation to the captions.
  118 
  119 ENDDOCUMENT();        # This should be the last executable line in the problem.
  120