# 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();