TrigFunctionsInDegrees

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Trigonometric Functions in Degrees in Student Answers


This PG code shows how to redefine trigonometric functions to evaluate in degrees rather than radians.

Problem Techniques Index

PG problem file Explanation
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
);
TEXT(beginproblem());

Initialization: We need to use MathObjects answer evaluators.

Context("Numeric");

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


Setup: WeBWorK's default is to evaluate trig functions in radians. Radians ought to 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.

These redefined functions allow students to enter inverse functions using syntax such as atan(x) and arctan(x), but not tan^(-1)(x). You may want to warn your students about this caveat in the main text section of the problem.

BEGIN_TEXT
Enter \( \sin(30) \): \{ ans_rule(20) \}
$BR
Enter \( \arcsin(1/2) \): \{ ans_rule(20) \}
$BR
Caution: Enter \( \arcsin(x) \) as \( \arcsin(x) \) or
\( \mathrm{asin}(x) \), but not \( \sin^{-1}(x) \).
END_TEXT

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

ANS( Real(0.5)->cmp() );
ANS( Real(30)->cmp() );

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

Answer Evaluation: As is the answer. We should include a comment that warns other instructors that trig functions are in degrees instead of radians.

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