View of /trunk/NationalProblemLibrary/ASU-topics/setTrigIdentities/srw7_3_53.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 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 0;
   32 
   33 $a = random(2,9,1);
   34 
   35 TEXT(EV2(<<EOT));
   36 Use the formula for lowering the powers to simplify the expression:
   37 $BR
   38 (a) If \( \cos^2 $a x - \sin^2 $a x = \cos (f(x)) \), then
   39 $BR
   40 \(f(x) =\) \{ans_rule(10)\};
   41 $BR
   42 (b) If \( \cos^4 $a x - \sin^4 $a x = \cos (g(x)) \), then
   43 $BR
   44 \(g(x) =\) \{ans_rule(10)\}.
   45 $BR
   46 $BBOLD
   47 Hint: $EBOLD For part (b), use  \( a^4-b^4=(a^2-b^2)(a^2+b^2) \)!
   48 
   49 $BR
   50 EOT
   51 
   52 $ans1= "2*$a*x";
   53 $ans2= "2*$a*x";
   54 
   55 ANS(fun_cmp($ans1));
   56 ANS(fun_cmp($ans2));
   57 
   58 ENDDOCUMENT();        # This should be the last executable line in the problem.