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Thu May 11 13:30:19 2006 UTC (7 years ago) by jjholt
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    1 ## DESCRIPTION
2 ## Precalculus: Trigonometry
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('trigonometry','inverse trigonometric functions')
6 ## Tagged by cmd6a 5/11/06
7
8 ## DBsubject('Precalculus')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Inverse Trigonometric Functions')
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"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33$pi = 4*atan2(1,1);
34
35 @values =('\pi/6','2\pi/3','5\pi/4','-\pi/3','-5\pi/6','-7\pi/4','7\pi/6','3\pi/4','5\pi/3');
36 $tag1 = random(0,8,1); 37$tag2 = random(0,8,1);
38 while ($tag2 ==$tag1) {$tag2 = random(0,8,1);} 39$tag3 = random(0,8,1);
40 $tag4 = random(0,8,1); 41 while ($tag4 == $tag3) {$tag4 = random(0,8,1);}
42
43 @arcsin_answers = (1/6, 1/3, -1/4, -1/3, -1/6, 1/4, -1/6, 1/4, -1/3);
44 @arccos_answers = (1/6, 2/3, 3/4, 1/3, 5/6, 1/4, 5/6, 3/4, 1/3);
45
46 TEXT(EV2(<<EOT));
47 Evaluate the following expressions. Your answer must be an angle
48 $$-\pi/2 \le \theta \le \pi$$ in radians, written as a multiple of $$\pi$$.
49 Note that $$\pi$$ is already
50 provided  in the answer so you simply have to fill in the appropriate multiple.
51 E.g. if the answer is $$\pi/2$$ you should enter 1/2. Do not use decimal answers.
52 Write the answer as a fraction or integer.$BR 53 $$\sin^{-1}(\sin((values[tag1]))$$ = 54 \{ans_rule(10) \} $$\pi$$ 55 EOT 56$ans = $arcsin_answers[$tag1];
57 ANS(exact_no_trig($ans)); 58 TEXT(EV2(<<EOT)); 59$BR
60 $$\sin^{-1}(\sin(values[tag2]))$$= \{ans_rule(10) \} $$\pi$$
61 EOT
62 $ans =$arcsin_answers[$tag2]; 63 ANS(exact_no_trig($ans));
64 TEXT(EV2(<<EOT));
65 $BR 66 $$\cos^{-1}(\cos(values[tag3]))$$= \{ans_rule(10) \} $$\pi$$ 67 EOT 68$ans = $arccos_answers[$tag3];
69 ANS(exact_no_trig($ans)); 70 TEXT(EV2(<<EOT)); 71$BR
72 $$\cos^{-1}(\cos(values[tag4]))$$= \{ans_rule(10) \} $$\pi$$
73 EOT
74 $ans =$arccos_answers[$tag4]; 75 ANS(exact_no_trig($ans));
76 ENDDOCUMENT();        # This should be the last executable line in the problem.
77


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