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# View of /trunk/NationalProblemLibrary/Rochester/setTrig07Identity/p8.pg

Wed Jun 28 22:52:53 2006 UTC (6 years, 10 months ago) by jj
File size: 1152 byte(s)
Fixed some tags.


    1 ## DESCRIPTION
2 ## Precalculus: Trigonometric Identities
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('trigonometry','half-angle')
6 ## Tagged by cmd6a 5/11/06
7
8 ## DBsubject('Trigonometry')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Double- and Half-Angle/Product-Sum Formulas')
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 "PGgraphmacros.pl",
29 "PGasu.pl"
30 );
31
32 TEXT(beginproblem());
33
34 $showPartialCorrectAnswers = 1; 35 36 37$a=random(2,8,1);
38
39
41
42
43 $ans1=3/8; 44$ans2=2*$a; 45$ans3=4*$a; 46 47 TEXT(EV2(<<EOT)); 48 Use half angle formulas to fill in the blanks in the identity below: 49 50$BR
51 $$(\sin(a x))^4$$ =
52 \{ans_rule(5) \}$$-\frac{1}{2}\cos($$ \{ans_rule(5) \} $$x ) 53 +\frac{1}{8}\cos ($$ \{ans_rule(5) \} $$x )$$
54
55 EOT
56
57 ANS(num_cmp($ans1)); 58 ANS(num_cmp($ans2));
59 ANS(num_cmp(\$ans3));
60
61
62 ENDDOCUMENT();        # This should be the last executable line in the problem.
63