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# View of /trunk/NationalProblemLibrary/Rochester/setTrig04FunctionsAnyAngle/ur_tr_1_8.pg

Thu Jun 29 19:14:59 2006 UTC (6 years, 10 months ago) by jj
File size: 1628 byte(s)
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 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 $showPartialCorrectAnswers = 1; 32 33$a = random(2,4,1);
34 $b = random($a+1,8,1);
35 $q = random(2,4,1); 36$pi = 3.1416;
37
38 if ($q == 2) { 39$s = 1;
40 $theta =$pi - arcsin($a/$b);
41 $quad = 'II'; 42 } 43 if ($q == 3) {
44 $s = -1; 45$theta = $pi + arcsin($a/$b); 46$quad = 'III';
47 }
48 if ($q == 4) { 49$s = -1;
50 $theta = 2*$pi - arcsin($a/$b);
51 $quad = 'IV'; 52 } 53 if ($s == 1) {$sign = ' '} 54 if ($s == -1) {$sign = '-'} 55 56 TEXT(EV2(<<EOT)); 57$PAR
58 If $$\sin( \theta ) = sign \frac {a} {b}$$, and $$\theta$$ is in quadrant $quad , then find 59$PAR
60 (a) $$\cos( \theta ) =$$ \{ ans_rule(15) \}
61 $PAR 62 (b) $$\tan( \theta ) =$$ \{ ans_rule(15) \} 63$PAR
64 (c) $$\sec( \theta ) =$$ \{ ans_rule(15) \}
65 $PAR 66 (d) $$\csc( \theta ) =$$ \{ ans_rule(15) \} 67$PAR
68 (e) $$\cot( \theta ) =$$ \{ ans_rule(15) \}
69 $PAR 70 71 EOT 72$ans_a = cos($theta); 73$ans_b = tan($theta); 74$ans_c = 1/$ans_a; 75$ans_d = $s *$b/$a; 76$ans_e = 1/$ans_b; 77 78 # record the answers 79 ANS(num_cmp([$ans_a,$ans_b,$ans_c,$ans_d,$ans_e], relTol=>.1));
80 ENDDOCUMENT(); # This should be the last executable line in the problem.