TrigFunctionsDegrees1: Difference between revisions

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(Modified to show the use of the TrigDegrees context.)
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<h2>Trig Functions in Degrees</h2>
<h2>Trigonometric Functions in Degrees</h2>


[[File:TrigFunctionsDegrees1.png|300px|thumb|right|Click to enlarge]]
[[File:TrigDegrees.png|300px|thumb|right|Click to enlarge]]
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
This PG code shows how to redefine trigonometric functions so they evaluate in degrees rather than radians.
This PG code shows how to use the context TrigDegrees to redefine trigonometric functions so they evaluate in degrees rather than radians.
</p>
</p>
* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Trig/TrigFunctionsDegrees1.pg FortLewis/Authoring/Templates/Trig/TrigFunctionsDegrees1.pg]
* File location in OPL: path to come <!--[https://github.com/openwebwork/webwork-open-problem-library/FIXPATH...TrigDegrees.pg  TrigDegrees.pg] -->
 
* PGML file location in OPL: path to come <!--[https://github.com/openwebwork/webwork-open-problem-library/FIXPATHtopgml...TrigDegreesPGML.pg TrigDegrees.pg] -->


<br clear="all" />
<br clear="all" />
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loadMacros(
loadMacros(
"PGstandard.pl",
  "PGstandard.pl",
"MathObjects.pl",
  "MathObjects.pl",
"AnswerFormatHelp.pl",
  "AnswerFormatHelp.pl",
  "contextTrigDegrees.pl",
  "PGcourse.pl",
);
);


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<p>
<p>
<b>Initialization:</b>
<b>Initialization:</b>
We need to use MathObjects answer evaluators.
We need to use MathObjects answer evaluators and to load the contextTrigDegrees macro.
</p>
</p>
</td>
</td>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
<td style="background-color:#ffffdd;border:black 1px dashed;">
<pre>
<pre>
Context("Numeric");
Context("TrigDegrees");
 
##############################################
#  Begin trig functions in degrees
 
Context()->functions->remove("cos");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub cos {
  shift; my $x = shift;
  return CORE::cos($x*3.14159265358979/180);
}
package main;
# Make it work on formulas as well as numbers
# if uncommented, this next line will generate error messages
#sub cos {Parser::Function->call('cos',@_)}
#  Add the new functions to the Context
Context()->functions->add( cos => {class => 'NewFunc', TeX => '\cos'}, );
 
 
Context()->functions->remove("sin");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub sin {
  shift; my $x = shift;
  return CORE::sin($x*3.14159265358979/180);
}
package main;
# Make it work on formulas as well as numbers
# if uncommented, this next line will generate error messages
#sub sin {Parser::Function->call('sin',@_)}
#  Add the new functions to the Context
Context()->functions->add( sin => {class => 'NewFunc', TeX => '\sin'}, );
 
 
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 $x = shift;
  return CORE::sin($x*3.14159265358979/180)/CORE::cos($x*3.14159265358979/180);
}
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'}, );
 
 
Context()->functions->remove("sec");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub sec {
  shift; my $x = shift;
  return 1.0/CORE::cos($x*3.14159265358979/180);
}
package main;
# Make it work on formulas as well as numbers
sub sec {Parser::Function->call('sec',@_)}
#  Add the new functions to the Context
Context()->functions->add( sec => {class => 'NewFunc', TeX => '\sec'}, );
 
 
Context()->functions->remove("csc");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub csc {
  shift; my $x = shift;
  return 1.0/CORE::sin($x*3.14159265358979/180);
}
package main;
# Make it work on formulas as well as numbers
sub csc {Parser::Function->call('csc',@_)}
#  Add the new functions to the Context
Context()->functions->add( csc => {class => 'NewFunc', TeX => '\csc'}, );
 
 
Context()->functions->remove("cot");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub cot {
  shift; my $x = shift;
  return CORE::cos($x*3.14159265358979/180)/CORE::sin($x*3.14159265358979/180);
}
package main;
# Make it work on formulas as well as numbers
sub cot {Parser::Function->call('cot',@_)}
#  Add the new functions to the Context
Context()->functions->add( cot => {class => 'NewFunc', TeX => '\cot'}, );
 
 
 
#sub asin {CORE::atan2($_[1],CORE::sqrt(1-$_[1]*$_[1]))}
#sub acos {CORE::atan2(CORE::sqrt(1-$_[1]*$_[1]),$_[1])}
#sub atan {CORE::atan2($_[1],1)}
#sub acot {CORE::atan2(1,$_[1])}
#sub asec {acos($_[0],1.0/$_[1])}
#sub acsc {asin($_[0],1.0/$_[1])}
 
 
Context()->functions->remove("acos");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub acos {CORE::atan2(CORE::sqrt(1-$_[1]*$_[1]),$_[1])*180/3.14159265358979}
package main;
# Make it work on formulas as well as numbers
sub acos {Parser::Function->call('acos',@_)}
#  Add the new functions to the Context
Context()->functions->add( acos => {class => 'NewFunc', TeX => '\arccos'}, );
 
 
Context()->functions->remove("asin");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub asin {CORE::atan2($_[1],CORE::sqrt(1-$_[1]*$_[1]))*180/3.14159265358979}
package main;
# Make it work on formulas as well as numbers
sub asin {Parser::Function->call('asin',@_)}
#  Add the new functions to the Context
Context()->functions->add( asin => {class => 'NewFunc', TeX => '\arcsin'}, );
 
 
Context()->functions->remove("atan");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub atan {CORE::atan2($_[1],1)*180/3.14159265358979}
package main;
# Make it work on formulas as well as numbers
sub atan {Parser::Function->call('atan',@_)}
#  Add the new functions to the Context
Context()->functions->add( atan => {class => 'NewFunc', TeX => '\arctan'}, );
 
 
Context()->functions->remove("asec");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub asec {CORE::atan2($_[1],CORE::sqrt(1-$_[1]*$_[1]))*180/3.14159265358979}
#sub asec {acos($_[0],1.0/$_[1])}
package main;
# Make it work on formulas as well as numbers
sub asec {Parser::Function->call('asec',@_)}
#  Add the new functions to the Context
Context()->functions->add( asec => {class => 'NewFunc', TeX => '\arcsec'}, );
 
 
Context()->functions->remove("acsc");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub acsc {CORE::atan2(CORE::sqrt(1-$_[1]*$_[1]),$_[1])*180/3.14159265358979}
#sub acsc {asin($_[0],1.0/$_[1])}
package main;
# Make it work on formulas as well as numbers
sub acsc {Parser::Function->call('acsc',@_)}
#  Add the new functions to the Context
Context()->functions->add( acsc => {class => 'NewFunc', TeX => '\arccsc'}, );
 
 
Context()->functions->remove("acot");
package NewFunc;
# this next line makes the function a
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub acot {CORE::atan2(1,$_[1])*180/3.14159265358979}
package main;
# Make it work on formulas as well as numbers
sub acot {Parser::Function->call('acot',@_)}
#  Add the new functions to the Context
Context()->functions->add( acot => {class => 'NewFunc', TeX => '\arccot'}, );
 
 
#  End trig functions in degrees
###################################################


$ans1 = Compute("sin(30)");
$ans2 = Compute("arcsin(0.5)");


</pre>
</pre>
Line 264: Line 75:
<p>
<p>
<b>Setup:</b>  
<b>Setup:</b>  
WeBWorK's default is to evaluate trig functions in radians.  Radians ought to
To override the WeBWorK default of evaluating trig functions in radians, use the TrigDegrees context, which redefines the standard trig functions to be in degrees, both in any formulas that appear later in the PG code and in any formulas that students
be used whenever possible.  Sometimes, degrees are unavoidable (e.g., when
your students are first learning trig and haven't yet been taught radians). 
The code in this section redefines the standard trig functions to be in degrees, both
in any formulas that appear later in the PG code and in any formulas that students
enter in answer blanks.
enter in answer blanks.
</p>
</p>
<p>
<p>
These redefined functions allow students to enter inverse functions using syntax such as
These redefined functions allow students to enter inverse functions using syntax such as
<code>atan(x)</code> and <code>arctan(x)</code>, but not <code>tan^(-1)(x)</code>.   
<code>atan(x)</code>, or <code>arctan(x)</code>, or <code>tan^(-1)(x)</code>.   
You may want to warn your students about this caveat in the main text section of the problem.
You may want to mention the syntax options in the main text section of the problem.
</p>
</p>
</td>
</td>
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\{ ans_rule(20) \}
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
\{ AnswerFormatHelp("formulas") \}
$BR
$PAR
Caution: Enter \( \arcsin(x) \) as \( \arcsin(x) \) or
Remark: Enter \( \arcsin(x) \) as arcsin(x), or
\( \mathrm{asin}(x) \), but not \( \sin^{-1}(x) \).
asin(x), or  sin^(-1)(x).
END_TEXT
END_TEXT
Context()->normalStrings;
Context()->normalStrings;
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$showPartialCorrectAnswers = 1;
$showPartialCorrectAnswers = 1;


ANS( Real(0.5)->cmp() );
ANS( $ans1->cmp() );
ANS( Real(30)->cmp() );
ANS( $ans2->cmp() );
</pre>
</pre>
<td style="background-color:#eeccff;padding:7px;">
<td style="background-color:#eeccff;padding:7px;">
<p>
<p>
<b>Answer Evaluation:</b>
<b>Answer Evaluation:</b>
As is the answer. We should include a comment that warns other instructors that trig functions are in degrees instead of radians.
The answers are 0.5 and 30 (computed in degrees in the Setup section).
</p>
</p>
</td>
</td>
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Context()->normalStrings;
Context()->normalStrings;


COMMENT("MathObject version.  Redefines trig functions to be in degrees (not radians).");
COMMENT("Redefines trig functions to be in degrees (not radians).");


ENDDOCUMENT();
ENDDOCUMENT();
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<td style="background-color:#ddddff;padding:7px;">
<td style="background-color:#ddddff;padding:7px;">
<p>
<p>
<b>Solution:</b>
<b>Solution:</b> Before ENDDOCUMENT, we should include a comment that warns other instructors that trig functions are in degrees instead of radians.
</p>
</p>
</td>
</td>

Revision as of 20:28, 22 July 2021

Trigonometric Functions in Degrees

Click to enlarge

This PG code shows how to use the context TrigDegrees to redefine trigonometric functions so they evaluate in degrees rather than radians.

  • File location in OPL: path to come
  • PGML file location in OPL: path to come


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "AnswerFormatHelp.pl",
  "contextTrigDegrees.pl",
  "PGcourse.pl",
);

TEXT(beginproblem());

Initialization: We need to use MathObjects answer evaluators and to load the contextTrigDegrees macro. 

Context("TrigDegrees");

$ans1 = Compute("sin(30)");
$ans2 = Compute("arcsin(0.5)");

Setup: To override the WeBWorK default of evaluating trig functions in radians, use the TrigDegrees context, which redefines the standard trig functions to be in degrees, both in any formulas that appear later in the PG code and in any formulas that students enter in answer blanks.

These redefined functions allow students to enter inverse functions using syntax such as atan(x), or arctan(x), or tan^(-1)(x). You may want to mention the syntax options in the main text section of the problem. 

Context()->texStrings;
BEGIN_TEXT
Enter \( \sin(30) \): 
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$BR
Enter \( \arcsin(1/2) \): 
\{ ans_rule(20) \}
\{ AnswerFormatHelp("formulas") \}
$PAR
Remark: Enter \( \arcsin(x) \) as  arcsin(x), or
asin(x), or  sin^(-1)(x).
END_TEXT
Context()->normalStrings;

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

$showPartialCorrectAnswers = 1;

ANS( $ans1->cmp() );
ANS( $ans2->cmp() );

Answer Evaluation: The answers are 0.5 and 30 (computed in degrees in the Setup section). 


Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT("Redefines trig functions to be in degrees (not radians).");

ENDDOCUMENT();

Solution: Before ENDDOCUMENT, we should include a comment that warns other instructors that trig functions are in degrees instead of radians.


Templates by Subject Area

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