PREP 2015 Question Authoring - Archived

Showing Trig Functions in the Answer

Showing Trig Functions in the Answer

by Daniele Arcara -
Number of replies: 2
I was working on a homework problem, and I ran into a problem when using trig functions. Let's say that I have the function f(x)=sin(2x), and I pick a random point x=a. Then, I ask them to compute the derivative, which would be 2cos(2a). Is there a way to display the answer as 2cos(2a) without manually entering it that way?

Here is my current code, which displays the answer as a decimal:

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "PGML.pl",
  "PGcourse.pl",
);

TEXT(beginproblem());

Context("Numeric");

$a = random(2,9,1);
$f = Formula("sin(2x)");
$g = $f->D;
$m = $g->eval(x => $a);

#######################################################
#
#  Find the derivative of f(x) = sin(2x) at a random point.
#

BEGIN_PGML
The derivative of [` f(x) = [$f] `] at [` x = [$a] `] is [_______]{"$m"}.
END_PGML

#######################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.
In reply to Daniele Arcara

Re: Showing Trig Functions in the Answer

by Davide Cervone -
When you use eval(), the answer will be numeric, and the structure of the formula from which it came will be lost. There is, however, a way to keep a formula that has the original structure. It requires that you turn off automatic reduction of constants, and use substitute() rather than eval(), at least for the first step. Here, 
    Context()->flags->set(
      reduceConstants => 0,
      reduceConstantFunctions => 0,
    );
    $m = $g->substitute(x=>$a);
would cause $m to be a formula that would display as 2 cos(2 a) where "a" is replaced by the value of $a.

But you don't want $m to be a formula, you want it to be a number, but still display as 2cos(2a). The correct answer string is actually a property of the MathObject itself, so you could evaluate it and set that correct answer string to

$m->string, but that is painful.

Fortunately, Compute() has a side-effect of note only evaluating the expression, but also setting the correct answer to be exactly the string that was passed to it. So Compute("2cos(2*$a)") would use the numeric value as the correct answer (not a formula) while still displaying 2cos(2*a) as the correct answer. So one approach here would be to do 

    Context()->flags->set(
      reduceConstants => 0,
      reduceConstantFunctions => 0,
    );
    $m = Compute($g->substitute(x=>$a)->string);
This will substitute $a into the original formula, turn the result back into a string, and the reparse that string as a MathObject, setting the correct answer to be the string with the substituted value.

Finally, note that you don't want to put quotes around $m in your PGML answer (as that would force the expression to be turned into a string again and re-parsed, which would lose the correct answer that you carefully set with Compute() above. So the crucial part of your problem would be 

Context("Numeric");
Context()->flags->set(
  reduceConstants => 0,
  reduceConstantFunctions => 0,
);

$a = random(2,9,1);
$f = Formula("sin(2x)");
$g = $f->D;
$m = Compute($g->substitute(x=>$a)->string);

#######################################################
#
#  Find the derivative of f(x) = sin(2x) at a random point.
#

BEGIN_PGML
The derivative of [` f(x) = [$f] `] at [` x = [$a] `] is [_______]{$m}.
END_PGML