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| 1 : | jjholt | 206 | ## DESCRIPTION |
| 2 : | ## Precalculus: Trigonometric Identities | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 141 | |
| 5 : | jjholt | 206 | ## KEYWORDS('trigonometry','half-angle') |
| 6 : | ## Tagged by cmd6a 5/11/06 | ||
| 7 : | |||
| 8 : | jj | 297 | ## DBsubject('Trigonometry') |
| 9 : | jjholt | 206 | ## 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 : | jj | 141 | DOCUMENT(); # This should be the first executable line in the problem. |
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.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 : | |||
| 40 : | #evaluate answers | ||
| 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 : |
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