View of /trunk/NationalProblemLibrary/Rochester/setTrig07Identity/p8.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometric Identities
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','half-angle')
    6 ## Tagged by cmd6a 5/11/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Analytic Trigonometry')
   10 ## DBsection('Double- and Half-Angle/Product-Sum Formulas')
   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 "PGgraphmacros.pl",
   29 "PGasu.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 
   34 $showPartialCorrectAnswers = 1;
   35 
   36 
   37 $a=random(2,8,1);
   38 
   39 
   40 #evaluate answers
   41 
   42 
   43 $ans1=3/8;
   44 $ans2=2*$a;
   45 $ans3=4*$a;
   46 
   47 TEXT(EV2(<<EOT));
   48 Use half angle formulas to fill in the blanks in the identity below:
   49 
   50 $BR
   51 \( (\sin($a x))^4 \) =
   52 \{ans_rule(5) \}\( -\frac{1}{2}\cos( \) \{ans_rule(5) \} \( x )
   53 +\frac{1}{8}\cos (  \) \{ans_rule(5) \} \(x ) \)
   54 
   55 EOT
   56 
   57 ANS(num_cmp($ans1));
   58 ANS(num_cmp($ans2));
   59 ANS(num_cmp($ans3));
   60 
   61 
   62 ENDDOCUMENT();        # This should be the last executable line in the problem.
   63