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Thu Jun 29 18:44:08 2006 UTC (6 years, 10 months ago) by jj
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Fixed tags.


    1 ##DESCRIPTION
2 ## Precalculus, Trigonometric Identities
3 ##ENDDESCRIPTION
4
5 ## KEYWORDS('precalculus','trigonometry','identities')
6 ## Tagged by skm9b
7
8 ## DBsubject('Trigonometry')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Trigonometric Identities')
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 "PGgraphmacros.pl",
29 "PGasu.pl"
30 );
31
32 TEXT(beginproblem());
33
34 $showPartialCorrectAnswers = 1; 35 36$pi = 4*atan2(1,1);
37 $a=random(3,9,2); 38$b=random($a+1,$a+2,1);
39
40 $cst=-$a/$b; 41 42 #evaluate answers 43 44$bb=$b**2; 45$d = $bb-$a**2;
46 $e = 2*$a**2-$bb; 47 48$snt="-sqrt($d)/$b";
49 $sn2t="2*$a*sqrt($d)/$bb";
50 $cs2t="$e/$bb"; 51$snthalf=sqrt((1-$cst)/2); 52$csthalf=-sqrt((1+$cst)/2); 53 54 TEXT(EV2(<<EOT)); 55 If $$\cos(t)=-\frac{a}{b}$$ where $$\pi < t < \frac{3\pi}{2}$$, find the 56 values of the following trigonometric functions. 57 58$BR
59 $BBOLD Note:$EBOLD
60 Give exact answers, do not use
61 decimal numbers. The answer should be a fraction or an arithmetic expression.
62 If the answer involves a square root it should be enter as sqrt; e.g. the square
63 root of 2 should be written as sqrt(2).
64
65 $BR 66$BR
67
68 $$\cos(2t)$$ =
69 \{ans_rule(20) \}
70 EOT
71
72 ANS(exact_no_trig($cs2t)); 73 TEXT(EV2(<<EOT)); 74$BR
75 $$\sin(2t)$$= \{ans_rule(20) \}
76 EOT
77 ANS(exact_no_trig($sn2t)); 78 TEXT(EV2(<<EOT)); 79$BR
80 $$\cos(\frac{t}{2})$$= \{ans_rule(20) \}
81 EOT
82 ANS(exact_no_trig($csthalf)); 83 84 TEXT(EV2(<<EOT)); 85$BR
86 $$\sin(\frac{t}{2})$$= \{ans_rule(20) \}
87 EOT
88
89 ANS(exact_no_trig(\$snthalf));
90 ENDDOCUMENT();        # This should be the last executable line in the problem.