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| 1 : | jj | 61 | ## DESCRIPTION |
| 2 : | ## Geometry: Plane Geometry | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('geometry', 'plane') | ||
| 6 : | ## Tagged by YJ | ||
| 7 : | |||
| 8 : | ## DBsubject('Geometry') | ||
| 9 : | ## DBchapter('Plane Geometry') | ||
| 10 : | ## DBsection('Trigonometric Identities') | ||
| 11 : | ## Date('5/26/2005') | ||
| 12 : | ## Author('Jeff Holt') | ||
| 13 : | ## Institution('UVA') | ||
| 14 : | ## TitleText1('Calculus') | ||
| 15 : | ## EditionText1('5e') | ||
| 16 : | ## AuthorText1('Stewart') | ||
| 17 : | ## Section1('5.8.4') | ||
| 18 : | ## Problem1(' ') | ||
| 19 : | |||
| 20 : | 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 : | $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. |
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