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    1 ## DESCRIPTION
2 ## Precalculus: Trigonometry
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('trigonometry','trigonometric equation')
6 ## Tagged by cmd6a 5/9/06
7
8 ## DBsubject('Precalculus')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Trigonometric Equations')
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 "PGasu.pl",
30 );
31
32 # No partial credit on this problem, so we say:
34
35 TEXT(beginproblem());
36 $showPartialCorrectAnswers = 0; 37$pi = 4*atan2(1,1);
38 @values =('\frac{1}{4}','\frac{3}{4}','\frac{1}{2}');
39 $tag1 = random(0,2,1); 40 41 42 @sin_answers1 = (1/6, 1/3, 1/4); 43 @sin_answers2 = (5/6, 2/3, 3/4); 44 @sin_answers3 = (7/6, 4/3, 5/4); 45 @sin_answers4 = (11/6, 5/3, 7/4); 46 47 48 49 TEXT(EV2(<<EOT)); 50 Solve the following equation in the interval [0, 2 $$\pi$$]. 51$BR
52 $BBOLD Note:$EBOLD
53 Give the answer as a multiple of $$\pi$$.
54 Do not use decimal numbers. The answer should be a fraction or an integer.
55 Note that $$\pi$$ is already included in the answer so you just have to
56 enter the appropriate multiple. E.g. if the answer is $$\pi/2$$ you should
57 enter  1/2.  If there is more than one answer enter them separated by commas.
58 $PAR 59 60 $$(\sin(t))^2=values[tag1]$$ 61$PAR
62 t = \{ans_rule(30) \}   $$\pi$$
63
64 EOT
65 $ans1 =$sin_answers1[$tag1]; 66$ans2 = $sin_answers2[$tag1];
67 $ans3 =$sin_answers3[$tag1]; 68$ans4 = $sin_answers4[$tag1];
69 ANS(no_decimal_list("$ans1,$ans2,$ans3,$ans4"));
70
71 ENDDOCUMENT();        # This should be the last executable line
72