TrigFunctionsInDegrees

Trigonometric Functions in Degrees in Student Answers

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

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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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