NAME
Math::Trig::Units - Inverse and hyperbolic trigonemetric Functions
in degrees, radians or gradians.
SYNOPSIS
use Math::Trig::Units qw(dsin dcos tan sec csc cot
asin acos atan asec acsc acot
sinh cosh tanh sech csch coth
asinh acosh atanh asech acsch acoth
deg_to_rad rad_to_deg
grad_to_rad rad_to_grad
deg_to_grad grad_to_deg
units zero approx);
$v = dsin($x);
$v = dcos($x);
$v = tan($x);
$v = sec($x);
$v = csc($x);
$v = cot($x);
$v = asin($x);
$v = acos($x);
$v = atan($x);
$v = asec($x);
$v = acsc($x);
$v = acot($x);
$v = sinh($x);
$v = cosh($x);
$v = tanh($x);
$v = sech($x);
$v = csch($x);
$v = coth($x);
$v = asinh($x);
$v = acosh($x);
$v = atanh($x);
$v = asech($x);
$v = acsch($x);
$v = acoth($x);
$degrees = rad_to_deg($radians);
$radians = deg_to_rad($degrees);
$degrees = grad_to_deg($gradians);
$gradians = deg_to_grad($degrees);
$radians = grad_to_rad($gradians);
$gradians = rad_to_grad($radians);
# set radians instead of degrees (default)
Math::Trig::Units::units('radians');
# set gradians as units
Math::Trig::Units::units('gradians');
# set degrees as units
Math::Trig::Units::units('degrees');
# return current unit setting
$units = Math::Trig::Units::units();
# set the factor that allows a function that is almost zero to be zero
# if int(func($x)*factor) == 0 then the function will be assumed to
# return zero rather than 0.00000000000001
Math::Trig::Units::zero(10e10);
# to make functions in degrees or radians return the expected value
# we can use the approx() function
approx(dsin(30)) == 0.5 # without approx it would be 0.49999999999999945
DESCRIPTION
This module exports the missing inverse and hyperbolic trigonometric functions of real numbers. The inverse functions return values cooresponding to the principal values. Specifying an argument outside of the domain of the function where an illegal divion by zero would occur will cause infinity to be returned. Infinity is Perl's version of this.
This module implements the functions in degrees by default. If you want radians use Math::Trig or set the units via the units sub:
# set radians instead of degrees (default)
Math::Trig::Units::units('radians');
# set gradians as units
Math::Trig::Units::units('gradians');
# set degrees as units
Math::Trig::Units::units('degrees');
# return current unit setting
$units = Math::Trig::Units::units();
A value of Pi to 30 decimal places is used in the source. This will be truncated by your version of Perl to the longest float supported.
To avoid redefining the internal sin() and cos() functions this module calls the functions dsin() and dcos().
units
Set the units. Options are 'radians', 'degrees', 'gradians' and are case insensitive. Alternatively you can call the subclasses
Math::Trig::Degree
Math::Trig::Radian
Math::Trig::Gradian
zero
If a function returns a value like 0.0000000000001 the correct value is in fact probably 0. When we have a 1/func() expression the return value should thus be #INF rather than some arbitarily large integer. To round very small numbers to zero for this purpose we use
int( func() * factor )
By default a factor or 1e12 is used so 1e-12 is not zero but 1e-13 is. You can set any factor you want although he default should work fine.
approx
Because of the limit on the accuracy of the vaule of Pi that is easily supported via a float you will get values like dsin(30) = 0.49999999999999945 when using degrees (or gradians). This can be fixed using the approx() function.
By default the approx sub will modify numbers so if we have a number like 0.499999945 with 6 9s or 0.50000012 with 6 0s the number will be rounded to 0.5. It also works on numbers like 5.250000001. This is useful when using degrees or gradians. In degrees these functions will return 0.5 as expected
approx(dsin(30))
approx(dcos(30))
The approx sub takes a second optional argument that specifies how many 0s or 9s in a row will trigger rounding. The default is 6.
approx($num, 7); # will return 0.5 for 0.500000001 but 0.50000001 if
# that is passed as it only has 6 zeros.
Numbers that do not fulfill the requisite criteria are returned unchanged. For example 0.5000001 will not be rounded to 0.5 as it only has 5 0s.
dsin
returns sin of real argument.
dcos
returns cos of real argument.
tan
returns tangent of real argument.
sec
returns secant of real argument.
csc
returns cosecant of real argument.
cot
returns cotangent of real argument.
asin
returns inverse sine of real argument.
acos
returns inverse cosine of real argument.
atan
returns inverse tangent of real argument.
asec
returns inverse secant of real argument.
acsc
returns inverse cosecant of real argument.
acot
returns inverse cotangent of real argument.
sinh
returns hyperbolic sine of real argument.
cosh
returns hyperbolic cosine of real argument.
tanh
returns hyperbolic tangent of real argument.
sech
returns hyperbolic secant of real argument.
csch
returns hyperbolic cosecant of real argument.
coth
returns hyperbolic cotangent of real argument.
asinh
returns inverse hyperbolic sine of real argument.
acosh
returns inverse hyperbolic cosine of real argument.
(positive value only)
atanh
returns inverse hyperbolic tangent of real argument.
asech
returns inverse hyperbolic secant of real argument.
(positive value only)
acsch
returns inverse hyperbolic cosecant of real argument.
acoth
returns inverse hyperbolic cotangent of real argument.
HISTORY
Modification of Math::Trig by request from stefan_k.
BUGS
Because of the limit on the accuracy of the vaule of Pi that is easily supported via a float you will get values like dsin(30) = 0.49999999999999945 when using degrees. This can be fixed using the approx() function
Let me know about any others.
AUTHOR
Initial Version John A.R. Williams <J.A.R.Williams@aston.ac.uk> Bug fixes and many additonal functions Jason Smith <smithj4@rpi.edu> This version James Freeman <james.freeman@id3.org.uk>