View of /trunk/NationalProblemLibrary/Rochester/setVecFunction1Curves/urvc_3_12.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('vector' 'velocity' 'parametric' 'tangent')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vector Functions')
   10 ## DBsection('Vector Functions and Space Curves')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   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 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a1 = random(-5,5,1);
   34 $pi =arccos(-1);
   35 
   36 BEGIN_TEXT
   37 $BR
   38  Find parametric equations for the tangent line at the point $BR
   39   \( (\cos(\frac{$a1 \pi}{6}) ,\sin(\frac{$a1 \pi}{6}) ,\frac{$a1 \pi}{6}) ) \)
   40   on the curve \( x=\cos t,\  y=\sin t, \ z=t \)
   41 $BR
   42 \( x(t) \) = \{ans_rule(40)\} $BR
   43 \( y(t) \)= \{ans_rule(40)\} $BR
   44 \( z(t) \)= \{ans_rule(40)\} $BR
   45 END_TEXT
   46 
   47 
   48 $ans0 =  "cos($a1*$pi/6)+(-sin($a1*$pi/6))*t" ;
   49 $ans1 =  "sin($a1*$pi/6)+(cos($a1*$pi/6))*t" ;
   50 $ans2 =  "$a1*$pi/6 +t" ;
   51 
   52 
   53 ANS(fun_cmp($ans0, vars=>"t"));
   54 ANS(fun_cmp($ans1, vars=>"t"));
   55 ANS(fun_cmp($ans2, vars=>"t"));
   56 
   57 ENDDOCUMENT();        # This should be the last executable line in the problem.