## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('cylindrical' 'coordinates') ## Tagged by tda2d ## DBsubject('Calculus') ## DBchapter('Multiple Integrals') ## DBsection('Change of a Variable, Cylindrical and Spherical Coordinates') ## Date('') ## Author('') ## Institution('Dartmouth') ## TitleText1('Basic Multivariable Calculus') ## EditionText1('') ## AuthorText1('Marsden, Tromba, and Weinstein') ## Section1('5.5') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem); $showPartialCorrectAnswers = 1;$a1 = random(0,10,1); $b1 = random(-10,10,1);$t1 = random(2,5,1); $t2 = random(3,10,2);$pi = arccos(-1); $theta =$t1*$pi/$t2; BEGIN_TEXT $PAR What are the rectangular coordinates of the point whose cylindrical coordinates are$BR $$(r= a1 ,\ \theta = \frac{t1 \pi}{t2} ,\ z= b1 )$$ ? $PAR$BR x= \{ans_rule(20)\} $BR y= \{ans_rule(20)\}$BR z= \{ans_rule(20)\} $BR END_TEXT$ans0 = $a1*cos($theta) ; $ans1 =$a1*sin($theta) ;$ans2 = $b1 ; &ANS(std_num_cmp($ans0)); &ANS(std_num_cmp($ans1)); &ANS(std_num_cmp($ans2)); ENDDOCUMENT(); # This should be the last executable line in the problem.