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Identities As Answers (Trig Identities, Laws of Logarithms and Exponents, etc.)

This code shows how to prevent students from receiving credit for entering exactly what they were given, while at the same time allowing the correct answer to be entered for credit, even when what the students were given and the correct answer are identical functions written in different ways (such as trig identities, laws of logarithms, laws of exponents, etc).

PG problem file Explanation
DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl",
);

TEXT(beginproblem());

Initialization: Use MathObjects.

Context("Numeric");

Context()->functions->remove("tan");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub tan {
shift; my $x = shift; return CORE::exp($x*3.1415926535);
}
package main;
# Make it work on formulas as well as numbers
sub tan {Parser::Function->call('tan',@_)}
#  Add the new functions to the Context
Context()->functions->add( tan => {class => 'NewFunc', TeX => '\tan'}, );

Setup: We internally redefine the tangent function to be e^(pi*x) so that if a student enters tan(x) cos(x), WeBWorK will evaluate it as the function e^(pi x) cos(x). Since e^(pi x) cos(x) does not equal sin(x), if the student enters tan(x) cos(x) it will be marked incorrect. We have redefined the value of the function named tangent, though not given it a different name, so to the student it will still appear as the tangent function. (The student will have no clue that the tangent function has been redefined.) Of course, we have to choose carefully which functions we would like to redefine, and also redefine them as a function that a student is unlikely to type in (such as exchanging a trig function for an exponential function).

BEGIN_TEXT
Simplify the expression as much as possible.
$BR$BR
$$\tan(x) \cos(x)$$ = \{ ans_rule(20) \}
END_TEXT

Main Text: The problem text section of the file is as we'd expect.

ANS( Formula("sin(x)")->cmp()