## DESCRIPTION
## Precalculus: Trigonometry
## ENDDESCRIPTION

## KEYWORDS('precalculus','trigonometric graphs')
## Tagged by cmd6a 6/21/06

## DBsubject('Trigonometry')
## DBchapter('Trigonometric Functions of Real Numbers')
## DBsection('Trigonometric Graphs')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGgraphmacros.pl",
"PGasu.pl"
);

TEXT(beginproblem());

$a=random(-4, -1);

$c=random(1, 8);
$b=1/$c;
$pi=4*arctan(1);
$xdom=3*$c;
$ydom=abs($a)+1;
$xgrid=2*$xdom;
$ygrid=2*$ydom;
$graph = init_graph(-$xdom,-$ydom,$xdom,$ydom,'axes'=>[0,0],'grid'=>[$xgrid,$ygrid]);
$f = FEQ("$a*cos($pi*$b*x) for x in <-$xdom,$xdom> using color:blue and weight:2");
($fref) = plot_functions( $graph, $f);
$period = 2*$c;

# Label some points
$label1 = new Label(0,$a, "$a",'black','right');
$d = -$a;
$label2 = new Label($c, $d, "($c,$d)",'black','bottom','center');
$label3 = new Label(0,$d,"$d",'black','top');
$graph->lb($label1, $label2, $label3);


BEGIN_TEXT
\{ image(insertGraph($graph)) \} $BR$BR
To get a better look at the graph, you can click on it.
$BR$BR

The curve above is the graph of a sinusoidal function.  It goes through
the point \( ($c,$d) \).  
Find a sinusoidal function that matches the given graph. If needed, you can enter
\(\pi\)  as $BITALIC pi$EITALIC in your answer.
$BR$BR
\(f(x) = \) \{ans_rule(60)\}
END_TEXT

#
# Tell WeBWork how to test if answers are right.  These should come in the
# same order as the answer blanks above.  You tell WeBWork both the type of
# "answer evaluator" to use, and the correct answer.
#
$ans = "$a*cos(pi*x/$c)";

ANS(fun_cmp($ans,limits=>[[-$xdom,$xdom]]));

ENDDOCUMENT();        # This should be the last executable line in the problem.