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| 1 : | jjholt | 156 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 134 | |
| 5 : | jjholt | 156 | ## KEYWORDS('cylindrical' 'coordinates') |
| 6 : | ## Tagged by tda2d | ||
| 7 : | jj | 134 | |
| 8 : | jjholt | 156 | ## DBsubject('Calculus') |
| 9 : | ## DBchapter('Multiple Integrals') | ||
| 10 : | ## DBsection('Change of a Variable, Cylindrical and Spherical Coordinates') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('Dartmouth') | ||
| 14 : | ## TitleText1('Basic Multivariable Calculus') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('Marsden, Tromba, and Weinstein') | ||
| 17 : | ## Section1('5.5') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | jj | 134 | 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 : | ); | ||
| 29 : | |||
| 30 : | TEXT(&beginproblem); | ||
| 31 : | $showPartialCorrectAnswers = 1; | ||
| 32 : | |||
| 33 : | $a1 = random(0,10,1); | ||
| 34 : | $b1 = random(-10,10,1); | ||
| 35 : | $t1 = random(2,5,1); | ||
| 36 : | $t2 = random(3,10,2); | ||
| 37 : | $pi = arccos(-1); | ||
| 38 : | $theta =$t1*$pi/$t2; | ||
| 39 : | |||
| 40 : | BEGIN_TEXT | ||
| 41 : | $PAR | ||
| 42 : | What are the rectangular coordinates of the point whose cylindrical coordinates | ||
| 43 : | are $BR \( (r= $a1 ,\ \theta = \frac{$t1 \pi}{$t2} ,\ z= $b1 ) \) ? | ||
| 44 : | $PAR | ||
| 45 : | $BR | ||
| 46 : | x= \{ans_rule(20)\} $BR | ||
| 47 : | y= \{ans_rule(20)\} $BR | ||
| 48 : | z= \{ans_rule(20)\} $BR | ||
| 49 : | END_TEXT | ||
| 50 : | |||
| 51 : | |||
| 52 : | $ans0 = $a1*cos($theta) ; | ||
| 53 : | $ans1 = $a1*sin($theta) ; | ||
| 54 : | $ans2 = $b1 ; | ||
| 55 : | |||
| 56 : | |||
| 57 : | &ANS(std_num_cmp($ans0)); | ||
| 58 : | &ANS(std_num_cmp($ans1)); | ||
| 59 : | &ANS(std_num_cmp($ans2)); | ||
| 60 : | |||
| 61 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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