View of /trunk/NationalProblemLibrary/Rochester/setTrig04FunctionsAnyAngle/p3.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','unit circle')
    6 ## Tagged by cmd6a 5/9/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Trigonometric Functions of Real Numbers')
   10 ## DBsection('The Unit Circle')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 #
   21 # First comes some stuff that appears at the beginning of every problem
   22 #
   23 
   24 DOCUMENT();        # This should be the first executable line in the problem.
   25 
   26 loadMacros(
   27 "PG.pl",
   28 "PGbasicmacros.pl",
   29 "PGchoicemacros.pl",
   30 "PGanswermacros.pl",
   31 "PGauxiliaryFunctions.pl",
   32 "PGasu.pl"
   33 );
   34 
   35 
   36 TEXT(beginproblem());
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $a = random(5,7,1);
   40 $b = random($a+1,12,1);
   41 $q = random(2,4,1);
   42 $pi = 3.1416;
   43 
   44 if ($q == 2) {
   45         $s = -1;
   46         $theta = $pi - arccos($a/$b);
   47         $quad = 'II';
   48         };
   49 if ($q == 3) {
   50         $s = -1;
   51         $theta = $pi + arccos($a/$b);
   52         $quad = 'III';
   53         };
   54 if ($q == 4) {
   55         $s = 1;
   56         $theta = 2*$pi - arccos($a/$b);
   57         $quad = 'IV';
   58         };
   59 if ($s == 1) {$sign = ' '};
   60 if ($s == -1) {$sign = '-'};
   61 
   62 TEXT(EV2(<<EOT));
   63 $PAR
   64 If \( \cos( \theta ) = $sign \frac {$a} {$b} \)
   65 and \( \theta \) is in quadrant $quad , then find
   66 $PAR
   67 (a)  \( \tan( \theta ) \cot( \theta ) = \) \{ ans_rule(15) \}
   68 $PAR
   69 (b)  \( \csc( \theta ) \tan( \theta ) = \) \{ ans_rule(15) \}
   70 $PAR
   71 (c)  \( \sin ^2 ( \theta ) + \cos ^2 ( \theta ) = \) \{ ans_rule(15) \}
   72 $PAR
   73 
   74 EOT
   75 $ans_a = 1;
   76 $ans_b = $s*$b/$a;
   77 $ans_c = 1;
   78 
   79 # record the answers
   80 ANS(num_cmp([$ans_a,$ans_b,$ans_c], relTol=>.1));
   81 ENDDOCUMENT();        # This should be the last executable line in the problem.
   82 
   83 
   84 
   85