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    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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