View of /trunk/NationalProblemLibrary/Rochester/setTrig04FunctionsAnyAngle/ur_tr_1_8.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','unit circle')
    6 ## Tagged by cmd6a 5/9/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Trigonometric Functions of Real Numbers')
   10 ## DBsection('The Unit Circle')
   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 $a = random(2,4,1);
   34 $b = random($a+1,8,1);
   35 $q = random(2,4,1);
   36 $pi = 3.1416;
   37 
   38 if ($q == 2) {
   39 $s = 1;
   40 $theta = $pi - arcsin($a/$b);
   41 $quad = 'II';
   42 }
   43 if ($q == 3) {
   44 $s = -1;
   45 $theta = $pi + arcsin($a/$b);
   46 $quad = 'III';
   47 }
   48 if ($q == 4) {
   49 $s = -1;
   50 $theta = 2*$pi - arcsin($a/$b);
   51 $quad = 'IV';
   52 }
   53 if ($s == 1) {$sign = ' '}
   54 if ($s == -1) {$sign = '-'}
   55 
   56 TEXT(EV2(<<EOT));
   57 $PAR
   58 If \( \sin( \theta ) = $sign \frac {$a} {$b} \), and \( \theta \) is in quadrant $quad , then find
   59 $PAR
   60 (a) \( \cos( \theta ) = \) \{ ans_rule(15) \}
   61 $PAR
   62 (b) \( \tan( \theta ) = \) \{ ans_rule(15) \}
   63 $PAR
   64 (c) \( \sec( \theta ) = \) \{ ans_rule(15) \}
   65 $PAR
   66 (d) \( \csc( \theta ) = \) \{ ans_rule(15) \}
   67 $PAR
   68 (e) \( \cot( \theta ) = \) \{ ans_rule(15) \}
   69 $PAR
   70 
   71 EOT
   72 $ans_a = cos($theta);
   73 $ans_b = tan($theta);
   74 $ans_c = 1/$ans_a;
   75 $ans_d = $s * $b/$a;
   76 $ans_e = 1/$ans_b;
   77 
   78 # record the answers
   79 ANS(num_cmp([$ans_a,$ans_b,$ans_c,$ans_d,$ans_e], relTol=>.1));
   80 ENDDOCUMENT(); # This should be the last executable line in the problem.