Disabling Functions

Disable functions and require exact fractions as answers.

Complete Code

POD for Macro Files

contextFraction.pl

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'contextFraction.pl', 'PGcourse.pl');

Preamble

The contextFraction.pl is loaded since we used the Fraction-NoDecimals context.

Context('Fraction-NoDecimals');

# Prevent pi from becoming 3.1415... and cos(pi) from
# becoming -1.
Context()->constants->set(pi => { keepName => 1 });

# The next context changes are not necessary to
# prevent cos(pi) from becoming -1, but they cannot hurt.
Context()->flags->set(
    reduceConstants         => 0,
    reduceConstantFunctions => 0
);

$f1 = Formula('cos(pi)');
$f2 = Formula('sin(pi/3)');

Context()->functions->disable('All');
Context()->functions->enable('sqrt');

$answer1 = Compute('-1');
$answer2 = Compute('sqrt(3)/2');

Setup

We choose a context that requires fractions as answers and does not allow decimals. After constructing the formulas involving trig functions, we disable all functions and re-enable the sqrt() function. This means that students are allowed to type in fractions and square roots, but not much else (e.g., they’ll get an error message if they type in a trig function).

Note that $f1 and $f2 are MathObject Formulas, which do not get reduced since pi is set to keep its name. If $f1 and $f2 used Compute instead, then the results would be -1 and 0.866… instead of cos() and sin(/3) as desired.

BEGIN_PGML
Enter your answers as simplified fractions.

+ [`[$f1] =`] [_]{$answer1}{15}

+ [`[$f2] =`] [_]{$answer2}{15}
END_PGML

Statement

This is the problem statement in PGML.

BEGIN_PGML_SOLUTION
The cosine of an angle is zero when the angle is an integer multiple of [`\pi`].
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.