## DESCRIPTION
## Precalculus: Trigonometry
## ENDDESCRIPTION

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

## DBsubject('Trigonometry')
## DBchapter('Analytic Trigonometry')
## DBsection('Trigonometric Equations')
## 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",
"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 =('\frac{3}{4}','\frac{1}{4}','\frac{1}{2}');
$tag1 = random(0,2,1);


@cos_answers1 = ("1/6",  "1/3", "1/4");
@cos_answers2 = ("5/6", "2/3", "3/4");
@cos_answers3 = ("7/6", "4/3", "5/4");
@cos_answers4 = ("11/6", "5/3", "7/4");



TEXT(EV2(<<EOT));
Solve the following equation 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

\( (\cos(t))^2=$values[$tag1] \)
$PAR
t = \{ans_rule(20) \}   \( \pi \)

EOT
$ans1 = $cos_answers1[$tag1];
$ans2 = $cos_answers2[$tag1];
$ans3 = $cos_answers3[$tag1];
$ans4 = $cos_answers4[$tag1];
ANS(no_decimal_list("$ans1,$ans2,$ans3,$ans4"));


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