View of /trunk/NationalProblemLibrary/Rochester/setTrig06Inverses/srw7_6_12-16c.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','inverse trigonometric functions')
    6 ## Tagged by cmd6a 5/11/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Analytic Trigonometry')
   10 ## DBsection('Inverse Trigonometric Functions')
   11 ## Date('')
   12 ## Author('')
   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 @values =('0','\frac{\sqrt{3}}{3}','1','\sqrt{3}');
   34 $tag1 = random(0,3,1);
   35 $tag2 = random(0,3,1);
   36 while ($tag2 == $tag1) {$tag2 = random(0,3,1);}
   37 
   38 @sin_arctan_answers = ( 0, 1/2, sqrt(2)/2,sqrt(3)/2);
   39 @cos_arctan_answers = ( 1, sqrt(3)/2, sqrt(2)/2, 1/2);
   40 
   41 TEXT(EV2(<<EOT));
   42 Evaluate the following expressions. $BR
   43 \( \sin(\tan^{-1}($values[$tag1])) \)
   44 \{ans_rule(20) \}
   45 EOT
   46 $ans = $sin_arctan_answers[$tag1];
   47 ANS(num_cmp($ans, mode=>"arith"));
   48 TEXT(EV2(<<EOT));
   49 $BR
   50 \( \cos(\tan^{-1}($values[$tag2])) \) \{ans_rule(20) \}
   51 EOT
   52 $ans = $cos_arctan_answers[$tag2];
   53 ANS(num_cmp($ans, mode=>"arith"));
   54 
   55 ENDDOCUMENT();        # This should be the last executable line in the problem.
   56