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# math::trig(n) 1.1 tcllib "Tcl Math Library"

## Name

math::trig - Trigonometric anf hyperbolic functions

## Synopsis

- package require Tcl 8.5 9
- package require math::trig 1.1

- ::math::trig::radian_reduced angle
- ::math::trig::degree_reduced angle
- ::math::trig::cosec angle
- ::math::trig::sec angle
- ::math::trig::cotan angle
- ::math::trig::acosec value
- ::math::trig::asec value
- ::math::trig::acotan value
- ::math::trig::cosech value
- ::math::trig::sech value
- ::math::trig::cotanh value
- ::math::trig::asinh value
- ::math::trig::acosh value
- ::math::trig::atanh value
- ::math::trig::acosech value
- ::math::trig::asech value
- ::math::trig::acotanh value
- ::math::trig::sind angle
- ::math::trig::cosd angle
- ::math::trig::tand angle
- ::math::trig::cosecd angle
- ::math::trig::secd angle
- ::math::trig::cotand angle

## Description

The math::trig package defines a set of trigonomic and hyperbolic functions and their inverses. In addition it defines versions of the trigonomic functions that take arguments in degrees instead of radians.

For easy use these functions may be imported into the tcl::mathfunc namespace, so that they can be used directly in the expr command.

## FUNCTIONS

The functions radian_reduced and degree_reduced return a reduced angle, in respectively radians and degrees, in the intervals [0, 2pi) and [0, 360):

::math::trig::radian_reduced angle

  Return the equivalent angle in the interval [0, 2pi).

  float angle

    Angle (in radians)

::math::trig::degree_reduced angle

  Return the equivalent angle in the interval [0, 360).

  float angle

    Angle (in degrees)

The following trigonomic functions are defined in addition to the ones defined in the expr command:

::math::trig::cosec angle

  Calculate the cosecant of the angle (1/cos(angle))

  float angle

    Angle (in radians)

::math::trig::sec angle

  Calculate the secant of the angle (1/sin(angle))

  float angle

    Angle (in radians)

::math::trig::cotan angle

  Calculate the cotangent of the angle (1/tan(angle))

  float angle

    Angle (in radians)

For these functions also the inverses are defined:

::math::trig::acosec value

  Calculate the arc cosecant of the value

  float value

    Value of the argument

::math::trig::asec value

  Calculate the arc secant of the value

  float value

    Value of the argument

::math::trig::acotan value

  Calculate the arc cotangent of the value

  float value

    Value of the argument

The following hyperbolic and inverse hyperbolic functions are defined:

::math::trig::cosech value

  Calculate the hyperbolic cosecant of the value (1/sinh(value))

  float value

    Value of the argument

::math::trig::sech value

  Calculate the hyperbolic secant of the value (1/cosh(value))

  float value

    Value of the argument

::math::trig::cotanh value

  Calculate the hyperbolic cotangent of the value (1/tanh(value))

  float value

    Value of the argument

::math::trig::asinh value

  Calculate the arc hyperbolic sine of the value

  float value

    Value of the argument

::math::trig::acosh value

  Calculate the arc hyperbolic cosine of the value

  float value

    Value of the argument

::math::trig::atanh value

  Calculate the arc hyperbolic tangent of the value

  float value

    Value of the argument

::math::trig::acosech value

  Calculate the arc hyperbolic cosecant of the value

  float value

    Value of the argument

::math::trig::asech value

  Calculate the arc hyperbolic secant of the value

  float value

    Value of the argument

::math::trig::acotanh value

  Calculate the arc hyperbolic cotangent of the value

  float value

    Value of the argument

The following versions of the common trigonometric functions and their inverses are defined:

::math::trig::sind angle

  Calculate the sine of the angle (in degrees)

  float angle

    Angle (in degrees)

::math::trig::cosd angle

  Calculate the cosine of the angle (in degrees)

  float angle

    Angle (in radians)

::math::trig::tand angle

  Calculate the cotangent of the angle (in degrees)

  float angle

    Angle (in degrees)

::math::trig::cosecd angle

  Calculate the cosecant of the angle (in degrees)

  float angle

    Angle (in degrees)

::math::trig::secd angle

  Calculate the secant of the angle (in degrees)

  float angle

    Angle (in degrees)

::math::trig::cotand angle

  Calculate the cotangent of the angle (in degrees)

  float angle

    Angle (in degrees)

## Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: trig of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.

When proposing code changes, please provide unified diffs, i.e the output of diff -u.

Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.

## Keywords

math, trigonometry

## Category

Mathematics

## Copyright

Copyright © 2018 Arjen Markus