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    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
22 loadMacros(
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
26 "PGanswermacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGasu.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34$a = random(3,7,2);
35 $b = random($a+1,$a+2,1); 36$q = random(2,4,1);
37 $pi = 3.1416; 38 39 if ($q == 2) {
40         $s = -1; 41$theta = $pi - arctan($b/$a); 42$inequality = '>';
43         };
44 if ($q == 3) { 45$s = 1;
46         $theta =$pi + arctan($b/$a);
47         $inequality = '<'; 48 }; 49 if ($q == 4) {
50         $s = -1; 51$theta = 2*$pi - arctan($b/$a); 52$inequality = '<';
53
54
55         };
56 if ($s == 1) {$sign = ' '};
57 if ($s == -1) {$sign = '-'};
58
59 TEXT(EV2(<<EOT));
60 Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS.
61 If the answer involves a square root it should be entered as $BITALIC sqrt$EITALIC.
62 For instance, the square
63 root of 2 should be written as sqrt(2).
64 $PAR 65 If $$\tan( \theta ) = sign \frac {b} {a}$$ 66 and $$\sin ( \theta ) inequality 0$$, then find 67$PAR
68 (a)  $$\sin( \theta ) =$$ \{ ans_rule(15) \}
69 $PAR 70 (b) $$\cos( \theta ) =$$ \{ ans_rule(15) \} 71$PAR
72 (c)  $$\sec( \theta ) =$$ \{ ans_rule(15) \}
73 $PAR 74 (d) $$\csc( \theta ) =$$ \{ ans_rule(15) \} 75$PAR
76 (e)  $$\cot( \theta ) =$$ \{ ans_rule(15) \}
77 $PAR 78 79 EOT 80$ans_a = sin($theta); 81 ANS(exact_no_trig($ans_a));
82 $ans_b = cos($theta);
83 ANS(exact_no_trig($ans_b)); 84$ans_c = 1/$ans_b; 85 ANS(exact_no_trig($ans_c));
86 $ans_d = 1/$ans_a;
87 ANS(exact_no_trig($ans_d)); 88$ans_e = $s*$a/$b; 89 ANS(exact_no_trig($ans_e));
90
91 # record the answers
92 ####ANS(num_cmp([$ans_a,$ans_b,$ans_c,$ans_d,\$ans_e], relTol=>.1));
93 ENDDOCUMENT();        # This should be the last executable line in the problem.


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