## DESCRIPTION
## Geometry: Plane Geometry
## ENDDESCRIPTION

## KEYWORDS('geometry', 'plane')
## Tagged by YJ

## DBsubject('Geometry')
## DBchapter('Plane Geometry')
## DBsection('Trigonometric Equations')
## Date('5/26/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.8.5')
## Problem1(' ')

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

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

# No partial credit on this problem, so we say:
install_problem_grader(~~&std_problem_grader);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 0;
$pi = 4*atan2(1,1);
@values =('{\sqrt(3)}','-{\sqrt(3)}','\frac{1}{\sqrt(3)}','-\frac{1}{\sqrt(3)}','1','-1');
$tag1 = random(0,5,1);
$tag2 = random(0,5,1);
while ($tag2 == $tag1) {$tag2 = random(0,5,1);}
$tag3 = random(0,5,1);
$tag4 = random(0,5,1);
while ($tag4 == $tag3) {$tag4 = random(0,5,1);}

@tan_answers1 = ("1/3",  "2/3", "1/6", "5/6","1/4", "3/4");
@tan_answers2 = ("4/3", "5/3", "7/6","11/6","5/4","7/4");

TEXT(EV2(<<EOT));
Solve the following equations in the interval [0, 2  \(\pi \)].
$BR
$BBOLD Note: $EBOLD
Give the answer as a multiple of \( \pi \). 
Do not use decimal numbers. The answer should be a fraction or an integer.
Note that \( \pi\) is already included in the answer so you just have to
enter the appropriate multiple. E.g. if the answer is \( \pi/2 \) you should
enter  1/2.  If there is more than one answer enter them separated by commas.
$PAR

\( \tan(t)=$values[$tag3] \)
$PAR
t = \{ans_rule(15) \}   \( \pi \)

EOT
$ans1 = $tan_answers1[$tag3];
$ans2 = $tan_answers2[$tag3];
&ANS(number_list_cmp("$ans1,$ans2"));

TEXT(EV2(<<EOT));
$PAR
\( \tan(t)=$values[$tag4] \)
$PAR
t = \{ans_rule(15) \} \( \pi\)

EOT
$ans1 = $tan_answers1[$tag4];
$ans2= $tan_answers2[$tag4];
&ANS(no_decimal_list("$ans1,$ans2"));


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