# DESCRIPTION
# Problem from H. J. Trussell for ECE200
# ENDDESCRIPTION
## DBsubject(Trigonometry)
## DBchapter(Trigonometric functions)
## DBsection(Trigonometric functions of special angles)
## Institution(Loyola University Chicago)
## Author(n/a)
## Level(2)
## KEYWORDS('tangent','sine','cosine')
DOCUMENT();
loadMacros(
"PGcourse.pl",
"PGstandard.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl", # needed for NchooseK(24,6)
#"PGanswermacros.pl",
#"PGauxiliaryFunctions.pl",
"extraAnswerEvaluators.pl"
);
TEXT(beginproblem());
Context("Numeric");
Parser::Number::NoDecimals();
$showPartialCorrectAnswers = 1;
@text_angle = ("\frac{\pi}{6}" , "\frac{\pi}{4}" , "\frac{\pi}{3}",
"\frac{2 \pi}{3}" , "\frac{3 \pi}{4}" , "\frac{5 \pi}{6}",
"\frac{7 \pi}{6}" , "\frac{5 \pi}{4}" , " \frac{4 \pi}{3}",
"\frac{5 \pi}{3}" , "\frac{7 \pi}{4}" , "\frac{11 \pi}{6}",
"\frac{-\pi}{6}" , "\frac{-\pi}{4}" , "\frac{-\pi}{3}",
"\frac{-2 \pi}{3}" , "\frac{-3 \pi}{4}" , "\frac{-5 \pi}{6}",
"\frac{-7 \pi}{6}" , "\frac{-5 \pi}{4}" , " \frac{-4 \pi}{3}",
"\frac{-5 \pi}{3}" , "\frac{-7 \pi}{4}" , "\frac{-11 \pi}{6}",);
@angle = (pi/6 , pi/4 , pi/3,
2*pi/3 , 3*pi/4 , 5*pi/6,
7*pi/6 , 5*pi/4 , 4*pi/3,
5*pi/3, 7*pi/4,11*pi/6,
-1*pi/6 ,-1* pi/4 , -1*pi/3,
-2*pi/3 , -3*pi/4 , -5*pi/6,
-7*pi/6 , -5*pi/4 , -4*pi/3,
-5*pi/3, -7*pi/4,-11*pi/6,);
@pick = NchooseK(24,6);
$ans1 = sin($angle[$pick[0]]);
$ans2 = sin($angle[$pick[1]]);
$ans3 = cos($angle[$pick[2]]);
$ans4 = cos($angle[$pick[3]]);
$ans5 = tan($angle[$pick[4]]);
$ans6 = tan($angle[$pick[5]]);
Context()->functions->disable("Trig");
BEGIN_TEXT
Practice finding the exact values of trig functions of common angles
$BR
$SPACE
$BR
Find the exact value of each without using a calculator. You may not enter decimals or use the trig functions in your answers. You can use fractions that contain integers and square roots.
$BR
$SPACE
$BR
a) \( \sin{ \left( $text_angle[$pick[0]] \right) } \) = \{ ans_rule(20) \}
$BR
b) \( \sin{ \left( $text_angle[$pick[1]] \right) } \) = \{ ans_rule(20) \}
$BR
c) \( \cos{ \left( $text_angle[$pick[2]] \right) } \) = \{ ans_rule(20) \}
$BR
d) \( \cos{ \left( $text_angle[$pick[3]] \right) } \) = \{ ans_rule(20) \}
$BR
e) \( \tan{ \left( $text_angle[$pick[4]] \right) } \) = \{ ans_rule(20) \}
$BR
f) \( \tan{ \left( $text_angle[$pick[5]] \right) } \) = \{ ans_rule(20) \}
$BR
END_TEXT
ANS( $ans1->cmp(tol=>0.00000000000001 ) );
ANS( $ans2->cmp(tol=>0.00000000000001) );
ANS( $ans3->cmp(tol=>0.00000000000001 ) );
ANS( $ans4->cmp(tol=>0.00000000000001 ) );
ANS($ans5->cmp(tol=>0.00000000000001 ) );
ANS($ans6->cmp(tol=>0.00000000000001 ) );
SOLUTION(EV3(<<'END_SOLUTION'));
$BR $SPACE $BR
$BBOLD SOLUTION $EBOLD
Note that answers are in decimal for now, will correct to fraction later
$BR
a) $SPACE \( \sin{ \left( $text_angle[$pick[0]] \right) } = $ans1 \)
$BR $SPACE $BR
b) $SPACE \( \sin{ \left( $text_angle[$pick[1]] \right) } = $ans2 \)
$BR $SPACE $BR
c) $SPACE \( \cos{ \left( $text_angle[$pick[2]] \right) } = $ans3 \)
$BR $SPACE $BR
d) $SPACE \( \cos{ \left( $text_angle[$pick[3]] \right) } = $ans4 \)
$BR $SPACE $BR
e) $SPACE \( \tan{ \left( $text_angle[$pick[4]] \right) } = $ans5 \)
$BR
f) $SPACE \( \tan{ \left( $text_angle[$pick[5]] \right) } = $ans6 \)
$BR
END_SOLUTION
COMMENT('MathObject version');
ENDDOCUMENT();