View of /trunk/NationalProblemLibrary/ASU-topics/setTrigInverse/p13.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','inverse trigonometric function')
    6 ## Tagged by cmd6a 6/22/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Analytic Trigonometry')
   10 ## DBsection('Inverse Trigonometric Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   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 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 @values =('\pi/6','2\pi/3','5\pi/4','-\pi/3','-5\pi/6','-7\pi/4','7\pi/6','3\pi/4','5\pi/3');
   35 
   36 $tag1 = random(0,8,1);
   37 $tag2 = random(0,8,1);
   38 while ($tag2 == $tag1) {$tag2 = random(0,8,1);}
   39 $tag3 = random(0,8,1);
   40 while ($tag3 == $tag2 or $tag3 == $tag1) {$tag3 = random(0,8,1);}
   41 $pi = 3.1415927;
   42 @arctan_answers = ("1/6", "-1/3", "1/4", "-1/3", "1/6", "1/4", "1/6", "-1/4", "-1/3");
   43 
   44 TEXT(EV2(<<EOT));
   45 Evaluate the following expressions. Your answer must be an angle in radians and in the interval \( [-\pi/2 , \pi/2 ] \).
   46 Note that \( \pi \) is already provided in the answer so you just have to write the
   47 appropriate multiple. E.g. if the answer is \( \pi /2 \) you should write 1/2.
   48 Do not use decimal numbers. The answer should be a fraction or an integer.
   49 $PAR
   50 (a) \( \tan^{-1}(\tan($values[$tag1])) = \) \{ans_rule(10) \}\( \pi\)
   51 EOT
   52 
   53 $ans = $arctan_answers[$tag1];
   54 ANS(exact_no_trig($ans));
   55 
   56 TEXT(EV2(<<EOT));
   57 $PAR
   58 (b) \( \tan^{-1}(\tan($values[$tag2])) = \) \{ans_rule(10) \} \( \pi\)
   59 EOT
   60 
   61 $ans = $arctan_answers[$tag2];
   62 ANS(exact_no_trig($ans));
   63 
   64 TEXT(EV2(<<EOT));
   65 $PAR
   66 (c) \( \tan^{-1}(\tan($values[$tag3])) = \) \{ans_rule(10) \} \( \pi\)
   67 EOT
   68 
   69 $ans = $arctan_answers[$tag3];
   70 ANS(exact_no_trig($ans));
   71 
   72 ENDDOCUMENT();        # This should be the last executable line in the problem.