View of /trunk/NationalProblemLibrary/ASU-topics/setTrigIdentities/p1.pg

    1 ##DESCRIPTION
    2 ## Precalculus, Trigonometric Identities
    3 ##ENDDESCRIPTION
    4 
    5 ## KEYWORDS('precalculus','trigonometry','identities')
    6 ## Tagged by skm9b
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Analytic Trigonometry')
   10 ## DBsection('Trigonometric Identities')
   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 "PGgraphmacros.pl",
   29 "PGasu.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $pi = 4*atan2(1,1);
   37 $a=random(3,9,2);
   38 $b=random($a+1,$a+2,1);
   39 
   40 $cst=-$a/$b;
   41 
   42 #evaluate answers
   43 
   44 $bb=$b**2;
   45 $d = $bb-$a**2;
   46 $e = 2*$a**2-$bb;
   47 
   48 $snt="-sqrt($d)/$b";
   49 $sn2t="2*$a*sqrt($d)/$bb";
   50 $cs2t="$e/$bb";
   51 $snthalf=sqrt((1-$cst)/2);
   52 $csthalf=-sqrt((1+$cst)/2);
   53 
   54 TEXT(EV2(<<EOT));
   55 If \( \cos(t)=-\frac{$a}{$b} \) where \( \pi < t < \frac{3\pi}{2} \), find the
   56 values of the following trigonometric functions.
   57 
   58 $BR
   59 $BBOLD Note: $EBOLD
   60 Give exact answers, do not use
   61 decimal numbers. The answer should be a fraction or an arithmetic expression.
   62 If the answer involves a square root it should be enter as sqrt; e.g. the square
   63 root of 2 should be written as sqrt(2).
   64 
   65 $BR
   66 $BR
   67 
   68 \( \cos(2t) \) =
   69 \{ans_rule(20) \}
   70 EOT
   71 
   72 ANS(exact_no_trig($cs2t));
   73 TEXT(EV2(<<EOT));
   74 $BR
   75 \( \sin(2t) \)= \{ans_rule(20) \}
   76 EOT
   77 ANS(exact_no_trig($sn2t));
   78 TEXT(EV2(<<EOT));
   79 $BR
   80 \( \cos(\frac{t}{2}) \)= \{ans_rule(20) \}
   81 EOT
   82 ANS(exact_no_trig($csthalf));
   83 
   84 TEXT(EV2(<<EOT));
   85 $BR
   86 \( \sin(\frac{t}{2}) \)= \{ans_rule(20) \}
   87 EOT
   88 
   89 ANS(exact_no_trig($snthalf));
   90 ENDDOCUMENT();        # This should be the last executable line in the problem.