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Mon May 22 17:36:35 2006 UTC (7 years ago) by jjholt
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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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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.