View of /trunk/NationalProblemLibrary/Rochester/setTrig05Graphs/p1.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('trigonometry','amplitude','period','phase shift')
    6 ## Tagged by cmd6a 5/10/06
    7 
    8 ## DBsubject('Precalculus')
    9 ## DBchapter('Trigonometric Functions of Real Numbers')
   10 ## DBsection('Trigonometric Graphs')
   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 $pi = 3.1416;
   34 $e = 2.71828;
   35 
   36 $a = random(17,24,1);
   37 $a_s = random(-1,1,2);
   38 if ($a_s == -1) {$a_sign = '-'};
   39 if ($a_s == 1) {$a_sign = ''};
   40 
   41 $b = random(2,9,1);
   42 
   43 $exp = non_zero_random(-4,4,1);
   44 $d   = $e ** $exp;
   45 $c_n = random(2,9,1);
   46 $c_s = random(-1,1,2);
   47 $c   = $c_s * $c_n * $d;
   48 
   49 if ($c_s == -1) {$c_sign = '-'};
   50 if ($c_s == 1) {$c_sign = '+'};
   51 
   52 TEXT(EV2(<<EOT));
   53 $PAR
   54 Let \( y = $a_sign \sqrt {$a} \sin($b \pi x $c_sign $c_n e ^{$exp} ) \).
   55 $PAR
   56 What is the amplitude?  \{ ans_rule(15) \}
   57 $PAR
   58 What is the period?  \{ ans_rule(15) \}
   59 $PAR
   60 What is the phase shift?  \{ ans_rule(15) \}
   61 $PAR
   62 [NOTE:  If needed, you can enter \(\pi\) as 'pi' in your answers.]
   63 
   64 EOT
   65 
   66 $ans_1 = sqrt($a);
   67 $ans_2 = 2 / $b;
   68 $ans_3 = -$c / ($pi*$b);
   69 
   70 # record the answers
   71 ANS(num_cmp([$ans_1,$ans_2,$ans_3], relTol=>.1));
   72 ENDDOCUMENT();        # This should be the last executable line in the problem.
   73