Difference between revisions of "TrigFunctionsDegrees1"

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−
<h2>Trig Functions in Degrees</h2>
 +
<h2>Trigonometric Functions in Degrees</h2>
   
−
<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
  
  +
[[File:TrigDegrees.png|300px|thumb|right|Click to enlarge]]
−
This PG code shows how to redefine trigonometric functions so they evaluate in degrees rather than radians.
  
  +
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
−
<ul>
  
  +
This PG code shows how to use the context TrigDegrees to redefine trigonometric functions so they evaluate in degrees rather than radians.
−
<li>Download file: [[File:TrigFunctionsDegrees1.txt]] (change the file extension from txt to pg when you save it)</li>
  
−
<li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/Trig/TrigFunctionsDegrees1.pg</code></li>
  
−
</ul>
  
 
</p>
  
</p>
  +
* File location in OPL: https://github.com/openwebwork/webwork-open-problem-library/tree/master/Contrib/ChamplainSaintLambert/Titcombe/TrigDegrees.pg <!--[https://github.com/openwebwork/webwork-open-problem-library/FIXPATH...TrigDegrees.pg TrigDegrees.pg] -->
  +
* PGML file location in OPL: https://github.com/openwebwork/webwork-open-problem-library/tree/master/Contrib/ChamplainSaintLambert/Titcombe/TrigDegreesPGML.pg <!--[https://github.com/openwebwork/webwork-open-problem-library/FIXPATHtopgml...TrigDegreesPGML.pg TrigDegrees.pg] -->
   
  +
<br clear="all" />
 
<p style="text-align:center;">
  
<p style="text-align:center;">
 
[[SubjectAreaTemplates|Templates by Subject Area]]
  
[[SubjectAreaTemplates|Templates by Subject Area]]
Line 40: Line 40:
 
<pre>
  
<pre>
 
DOCUMENT();
  
DOCUMENT();
  +
 
loadMacros(
  
loadMacros(
−
"PGstandard.pl",
 +
"PGstandard.pl",
−
"MathObjects.pl",
 +
"MathObjects.pl",
  +
"AnswerFormatHelp.pl",
  +
"contextTrigDegrees.pl",
  +
"PGcourse.pl",
 
);
  
);
  +
 
TEXT(beginproblem());
  
TEXT(beginproblem());
 
</pre>
  
</pre>
Line 50: Line 52:
 
<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>
Line 60: Line 62:
 
<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 68: Line 72:
 
<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>
Line 90: Line 90:
 
Context()->texStrings;
  
Context()->texStrings;
 
BEGIN_TEXT
  
BEGIN_TEXT
−
Enter \( \sin(30) \): \{ ans_rule(20) \}
 +
Enter \( \sin(30) \):
−
$BR
 +
\{ ans_rule(20) \}
−
Enter \( \arcsin(1/2) \): \{ ans_rule(20) \}
 +
\{ AnswerFormatHelp("formulas") \}
 
$BR
  
$BR
−
Caution: Enter \( \arcsin(x) \) as \( \arcsin(x) \) or
 +
Enter \( \arcsin(1/2) \):
−
\( \mathrm{asin}(x) \), but not \( \sin^{-1}(x) \).
 +
\{ ans_rule(20) \}
  +
\{ AnswerFormatHelp("formulas") \}
  +
$PAR
  +
Remark: Enter \( \arcsin(x) \) as arcsin(x), or
  +
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( Compute("pi/6")->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>
Line 139: Line 139:
 
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>
Line 158: Line 158:
   
 
[[Category:Top]]
  
[[Category:Top]]
−
[[Category:Authors]]
 +
[[Category:Sample Problems]]
  +
[[Category:Subject Area Templates]]
  +
[[Category:Problem Techniques]]

Revision as of 12:57, 24 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.


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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