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# View of /trunk/NationalProblemLibrary/ASU-topics/setTrigInverse/p13.pg

Tue Aug 8 13:51:04 2006 UTC (6 years, 10 months ago) by jj
File size: 1956 byte(s)
Tag fixing; precalculus --> trigonometry


    1 ## DESCRIPTION
2 ## Precalculus: Trigonometry
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('trigonometry','inverse trigonometric function')
6 ## Tagged by cmd6a 6/22/06
7
8 ## DBsubject('Trigonometry')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Inverse Trigonometric Functions')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
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 $showPartialCorrectAnswers = 1; 33 34 @values =('\pi/6','2\pi/3','5\pi/4','-\pi/3','-5\pi/6','-7\pi/4','7\pi/6','3\pi/4','5\pi/3'); 35 36$tag1 = random(0,8,1);
37 $tag2 = random(0,8,1); 38 while ($tag2 == $tag1) {$tag2 = random(0,8,1);}
39 $tag3 = random(0,8,1); 40 while ($tag3 == $tag2 or$tag3 == $tag1) {$tag3 = random(0,8,1);}
41 $pi = 3.1415927; 42 @arctan_answers = ("1/6", "-1/3", "1/4", "-1/3", "1/6", "1/4", "1/6", "-1/4", "-1/3"); 43 44 TEXT(EV2(<<EOT)); 45 Evaluate the following expressions. Your answer must be an angle in radians and in the interval $$[-\pi/2 , \pi/2 ]$$. 46 Note that $$\pi$$ is already provided in the answer so you just have to write the 47 appropriate multiple. E.g. if the answer is $$\pi /2$$ you should write 1/2. 48 Do not use decimal numbers. The answer should be a fraction or an integer. 49$PAR
50 (a) $$\tan^{-1}(\tan(values[tag1])) =$$ \{ans_rule(10) \}$$\pi$$
51 EOT
52
53 $ans =$arctan_answers[$tag1]; 54 ANS(exact_no_trig($ans));
55
56 TEXT(EV2(<<EOT));
57 $PAR 58 (b) $$\tan^{-1}(\tan(values[tag2])) =$$ \{ans_rule(10) \} $$\pi$$ 59 EOT 60 61$ans = $arctan_answers[$tag2];
62 ANS(exact_no_trig($ans)); 63 64 TEXT(EV2(<<EOT)); 65$PAR
66 (c) $$\tan^{-1}(\tan(values[tag3])) =$$ \{ans_rule(10) \} $$\pi$$
67 EOT
68
69 $ans =$arctan_answers[$tag3]; 70 ANS(exact_no_trig($ans));
71
72 ENDDOCUMENT();        # This should be the last executable line in the problem.