View of /trunk/NationalProblemLibrary/Rochester/setTrig08Equations/p1.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','trigonometric equation')
    6 ## Tagged by cmd6a 5/9/06
    7 
    8 ## DBsubject('Precalculus')
    9 ## DBchapter('Analytic Trigonometry')
   10 ## DBsection('Trigonometric Equations')
   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 "PGasu.pl",
   29 "extraAnswerEvaluators.pl"
   30 );
   31 
   32 # No partial credit on this problem, so we say:
   33 install_problem_grader(~~&std_problem_grader);
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 0;
   37 $pi = 4*atan2(1,1);
   38 @values =('\frac{1}{4}','\frac{3}{4}','\frac{1}{2}');
   39 $tag1 = random(0,2,1);
   40 
   41 
   42 @sin_answers1 = (1/6,  1/3, 1/4);
   43 @sin_answers2 = (5/6, 2/3, 3/4);
   44 @sin_answers3 = (7/6, 4/3, 5/4);
   45 @sin_answers4 = (11/6, 5/3, 7/4);
   46 
   47 
   48 
   49 TEXT(EV2(<<EOT));
   50 Solve the following equation in the interval [0, 2  \(\pi \)].
   51 $BR
   52 $BBOLD Note: $EBOLD
   53 Give the answer as a multiple of \( \pi \).
   54 Do not use decimal numbers. The answer should be a fraction or an integer.
   55 Note that \( \pi\) is already included in the answer so you just have to
   56 enter the appropriate multiple. E.g. if the answer is \( \pi/2 \) you should
   57 enter  1/2.  If there is more than one answer enter them separated by commas.
   58 $PAR
   59 
   60 \( (\sin(t))^2=$values[$tag1] \)
   61 $PAR
   62 t = \{ans_rule(30) \}   \( \pi \)
   63 
   64 EOT
   65 $ans1 = $sin_answers1[$tag1];
   66 $ans2 = $sin_answers2[$tag1];
   67 $ans3 = $sin_answers3[$tag1];
   68 $ans4 = $sin_answers4[$tag1];
   69 ANS(no_decimal_list("$ans1,$ans2,$ans3,$ans4"));
   70 
   71 ENDDOCUMENT();        # This should be the last executable line
   72