View of /trunk/NationalProblemLibrary/Rochester/setTrig06Inverses/p12.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('Precalculus')
    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 "PGasu.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 $pi = 4*atan2(1,1);
   34 
   35 @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');
   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 $tag4 = random(0,8,1);
   41 while ($tag4 == $tag3) {$tag4 = random(0,8,1);}
   42 
   43 @arcsin_answers = (1/6, 1/3, -1/4, -1/3, -1/6, 1/4, -1/6, 1/4, -1/3);
   44 @arccos_answers = (1/6, 2/3, 3/4, 1/3, 5/6, 1/4, 5/6, 3/4, 1/3);
   45 
   46 TEXT(EV2(<<EOT));
   47 Evaluate the following expressions. Your answer must be an angle
   48 \( -\pi/2 \le \theta \le \pi \) in radians, written as a multiple of \(\pi\).
   49 Note that \( \pi\) is already
   50 provided  in the answer so you simply have to fill in the appropriate multiple.
   51 E.g. if the answer is \( \pi/2 \) you should enter 1/2. Do not use decimal answers.
   52 Write the answer as a fraction or integer.$BR
   53 \( \sin^{-1}(\sin(($values[$tag1])) \) =
   54 \{ans_rule(10) \} \( \pi \)
   55 EOT
   56 $ans = $arcsin_answers[$tag1];
   57 ANS(exact_no_trig($ans));
   58 TEXT(EV2(<<EOT));
   59 $BR
   60 \( \sin^{-1}(\sin($values[$tag2])) \)= \{ans_rule(10) \} \( \pi\)
   61 EOT
   62 $ans = $arcsin_answers[$tag2];
   63 ANS(exact_no_trig($ans));
   64 TEXT(EV2(<<EOT));
   65 $BR
   66 \( \cos^{-1}(\cos($values[$tag3])) \)= \{ans_rule(10) \}  \( \pi \)
   67 EOT
   68 $ans = $arccos_answers[$tag3];
   69 ANS(exact_no_trig($ans));
   70 TEXT(EV2(<<EOT));
   71 $BR
   72 \( \cos^{-1}(\cos($values[$tag4])) \)= \{ans_rule(10) \} \( \pi \)
   73 EOT
   74 $ans = $arccos_answers[$tag4];
   75 ANS(exact_no_trig($ans));
   76 ENDDOCUMENT();        # This should be the last executable line in the problem.
   77