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Thu Jun 29 19:14:59 2006 UTC (6 years, 11 months ago) by jj
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Fixed tags.


    1 ## DESCRIPTION
2 ## Precalculus: Trigonometry
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('trigonometry','unit circle')
6 ## Tagged by cmd6a 5/9/06
7
8 ## DBsubject('Trigonometry')
9 ## DBchapter('Trigonometric Functions of Real Numbers')
10 ## DBsection('The Unit Circle')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 #
21 # First comes some stuff that appears at the beginning of every problem
22 #
23
24 DOCUMENT();        # This should be the first executable line in the problem.
25
27 "PG.pl",
28 "PGbasicmacros.pl",
29 "PGchoicemacros.pl",
31 "PGauxiliaryFunctions.pl",
32 "PGasu.pl"
33 );
34
35
36 TEXT(beginproblem());
37 $showPartialCorrectAnswers = 1; 38 39$a = random(5,7,1);
40 $b = random($a+1,12,1);
41 $q = random(2,4,1); 42$pi = 3.1416;
43
44 if ($q == 2) { 45$s = -1;
46         $theta =$pi - arccos($a/$b);
47         $quad = 'II'; 48 }; 49 if ($q == 3) {
50         $s = -1; 51$theta = $pi + arccos($a/$b); 52$quad = 'III';
53         };
54 if ($q == 4) { 55$s = 1;
56         $theta = 2*$pi - arccos($a/$b);
57         $quad = 'IV'; 58 }; 59 if ($s == 1) {$sign = ' '}; 60 if ($s == -1) {$sign = '-'}; 61 62 TEXT(EV2(<<EOT)); 63$PAR
64 If $$\cos( \theta ) = sign \frac {a} {b}$$
65 and $$\theta$$ is in quadrant $quad , then find 66$PAR
67 (a)  $$\tan( \theta ) \cot( \theta ) =$$ \{ ans_rule(15) \}
68 $PAR 69 (b) $$\csc( \theta ) \tan( \theta ) =$$ \{ ans_rule(15) \} 70$PAR
71 (c)  $$\sin ^2 ( \theta ) + \cos ^2 ( \theta ) =$$ \{ ans_rule(15) \}
72 $PAR 73 74 EOT 75$ans_a = 1;
76 $ans_b =$s*$b/$a;
77 $ans_c = 1; 78 79 # record the answers 80 ANS(num_cmp([$ans_a,$ans_b,$ans_c], relTol=>.1));
81 ENDDOCUMENT();        # This should be the last executable line in the problem.
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