View of /trunk/NationalProblemLibrary/ASU-topics/setTrigGraphs/p23.pg

    1 ## DESCRIPTION
    2 ## Geometry: Plane Geometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('geometry', 'plane')
    6 ## Tagged by YJ
    7 
    8 ## DBsubject('Geometry')
    9 ## DBchapter('Plane Geometry')
   10 ## DBsection('Trigonometric Functions')
   11 ## Date('5/26/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('5.8.2')
   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 "PGgraphmacros.pl",
   29 "PGasu.pl"
   30 );
   31 
   32 TEXT(&beginproblem);
   33 
   34 $a=random(-4, -1);
   35 
   36 $c=random(1, 8);
   37 $b=1/$c;
   38 $pi=4*arctan(1);
   39 $xdom=3*$c;
   40 $ydom=abs($a)+1;
   41 $xgrid=2*$xdom;
   42 $ygrid=2*$ydom;
   43 $graph = init_graph(-$xdom,-$ydom,$xdom,$ydom,'axes'=>[0,0],'grid'=>[$xgrid,$ygrid]);
   44 $f = FEQ("$a*cos($pi*$b*x) for x in <-$xdom,$xdom> using color:blue and weight:2");
   45 ($fref) = plot_functions( $graph, $f);
   46 $period = 2*$c;
   47 
   48 # Label some points
   49 $label1 = new Label(0,$a, "$a",'black','right');
   50 $d = -$a;
   51 $label2 = new Label($c, $d, "($c,$d)",'black','bottom','center');
   52 $label3 = new Label(0,$d,"$d",'black','top');
   53 $graph->lb($label1, $label2, $label3);
   54 
   55 
   56 BEGIN_TEXT
   57 \{ image(insertGraph($graph)) \} $PAR
   58 To get a better look at the graph, you can click on it.
   59 $PAR
   60 
   61 
   62 The curve above is the graph of a sinusoidal function.  It goes through
   63 the point \( ($c,$d) \).
   64 Find a sinusoidal function that matches the given graph. If needed, you can enter
   65 \(\pi\)=3.1416...  as 'pi' in your answer, otherwise use at least 3 decimal digits.
   66 $PAR
   67   \(f(x) = \) \{ans_rule(60)\}
   68 END_TEXT
   69 
   70 #
   71 # Tell WeBWork how to test if answers are right.  These should come in the
   72 # same order as the answer blanks above.  You tell WeBWork both the type of
   73 # "answer evaluator" to use, and the correct answer.
   74 #
   75 $ans = "$a*cos($pi*$b*x)";
   76 
   77 &ANS(function_cmp($ans,"x",-$xdom,$xdom));
   78 
   79 ENDDOCUMENT();        # This should be the last executable line in the problem.
   80