View of /trunk/NationalProblemLibrary/Rochester/setTrig07Identity/srw7_1_35.pg

    1 ##DESCRIPTION
    2 ## Algebra: Analytic Trigonometry
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'analytic trigonometry', 'trigonometric identities')
    6 
    7 ## tcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Trigonometry')
   10 ## DBchapter('Analytic Trigonometry')
   11 ## DBsection('Trigonometric Identities')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Precalculus')
   16 ## EditionText1('3')
   17 ## AuthorText1('Stewart, Redlin, Watson')
   18 ## Section1('7.1')
   19 ## Problem1('33')
   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 "MathObjects.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 0;
   33 
   34 
   35 Context('Numeric');
   36 Context()->variables->add(y=>'Real');
   37 Context()->functions->undefine('sqrt');
   38 Context()->operators->undefine('**','^');
   39 
   40 BEGIN_TEXT
   41 Simplify and write the trigonometric expression in terms of sine and cosine:
   42 $BR
   43 \[ (1-\cos y)(1+\cos y)  = (f(y))^2 \]
   44 $BR
   45 \(f(y)=\) \{ans_rule(20)\}.
   46 END_TEXT
   47 
   48 sub mycheck {
   49   my ($correct, $student) = @_;
   50   $student = Formula($student);
   51   $correct = Formula($correct);
   52   return 1 if abs($student)==abs($correct);
   53   return 0;
   54 }
   55 
   56 $ans = Formula("sin(y)");
   57 ANS( $ans->cmp( checker => ~~&mycheck ) );
   58 
   59 ENDDOCUMENT();        # This should be the last executable line in the problem.