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# Annotation of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh1S6/urvc_3_1a.pg

 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.