View of /trunk/NationalProblemLibrary/Rochester/setTrig04FunctionsAnyAngle/p10.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 "PGasu.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = random(3,7,2);
   35 $b = random($a+1,$a+2,1);
   36 $q = random(2,4,1);
   37 $pi = 3.1416;
   38 
   39 if ($q == 2) {
   40         $s = -1;
   41         $theta = $pi - arctan($b/$a);
   42         $inequality = '>';
   43         };
   44 if ($q == 3) {
   45         $s = 1;
   46         $theta = $pi + arctan($b/$a);
   47         $inequality = '<';
   48         };
   49 if ($q == 4) {
   50         $s = -1;
   51         $theta = 2*$pi - arctan($b/$a);
   52         $inequality = '<';
   53 
   54 
   55         };
   56 if ($s == 1) {$sign = ' '};
   57 if ($s == -1) {$sign = '-'};
   58 
   59 TEXT(EV2(<<EOT));
   60 Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS.
   61 If the answer involves a square root it should be entered as $BITALIC sqrt $EITALIC.
   62 For instance, the square
   63 root of 2 should be written as sqrt(2).
   64 $PAR
   65 If \( \tan( \theta ) = $sign \frac {$b} {$a} \)
   66 and \( \sin ( \theta ) $inequality 0 \), then find
   67 $PAR
   68 (a)  \( \sin( \theta ) = \) \{ ans_rule(15) \}
   69 $PAR
   70 (b)  \( \cos( \theta ) = \) \{ ans_rule(15) \}
   71 $PAR
   72 (c)  \( \sec( \theta ) = \) \{ ans_rule(15) \}
   73 $PAR
   74 (d)  \( \csc( \theta ) = \) \{ ans_rule(15) \}
   75 $PAR
   76 (e)  \( \cot( \theta ) = \) \{ ans_rule(15) \}
   77 $PAR
   78 
   79 EOT
   80 $ans_a = sin($theta);
   81 ANS(exact_no_trig($ans_a));
   82 $ans_b = cos($theta);
   83 ANS(exact_no_trig($ans_b));
   84 $ans_c = 1/$ans_b;
   85 ANS(exact_no_trig($ans_c));
   86 $ans_d = 1/$ans_a;
   87 ANS(exact_no_trig($ans_d));
   88 $ans_e = $s*$a/$b;
   89 ANS(exact_no_trig($ans_e));
   90 
   91 # record the answers
   92 ####ANS(num_cmp([$ans_a,$ans_b,$ans_c,$ans_d,$ans_e], relTol=>.1));
   93 ENDDOCUMENT();        # This should be the last executable line in the problem.