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# View of /trunk/NationalProblemLibrary/Rochester/setTrig04FunctionsAnyAngle/ur_tr_1_9.pg

Thu Jun 29 19:14:59 2006 UTC (6 years, 10 months ago) by jj
File size: 1641 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 - arctan($b/$a);
41 $inequality = '>'; 42 } 43 if ($q == 3) {
44 $s = 1; 45$theta = $pi + arctan($b/$a); 46$inequality = '<';
47 }
48 if ($q == 4) { 49$s = -1;
50 $theta = 2*$pi - arctan($b/$a);
51 $inequality = '<'; 52 } 53 if ($s == 1) {$sign = ' '} 54 if ($s == -1) {$sign = '-'} 55 56 TEXT(EV2(<<EOT)); 57$PAR
58 If $$\tan( \theta ) = sign \frac {b} {a}$$
59 and $$\sin ( \theta ) inequality 0$$, then find
60 $PAR 61 (a) $$\sin( \theta ) =$$ \{ ans_rule(15) \} 62$PAR
63 (b) $$\cos( \theta ) =$$ \{ ans_rule(15) \}
64 $PAR 65 (c) $$\sec( \theta ) =$$ \{ ans_rule(15) \} 66$PAR
67 (d) $$\csc( \theta ) =$$ \{ ans_rule(15) \}
68 $PAR 69 (e) $$\cot( \theta ) =$$ \{ ans_rule(15) \} 70$PAR
71
72 EOT
73 $ans_a = sin($theta);
74 $ans_b = cos($theta);
75 $ans_c = 1/$ans_b;
76 $ans_d = 1/$ans_a;
77 $ans_e =$s*$a/$b;
78
80 ANS(num_cmp([$ans_a,$ans_b,$ans_c,$ans_d,\$ans_e], relTol=>.1));