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Trigonometric functions
=======================================================================





Sine, `x` in degrees, `\mathrm{sind}(x)`
-------------------------------------------------------------------------------

.. method:: math53.sind(x)

    Returns the sine of `x`, with `x` in degrees, `\mathrm{sind}(x)`.  See also  Wikipedia :cite:p:`WikipediaFun31`,  MathWorld :cite:p:`WolframFun31`,  NIST :cite:p:`DLMFun30`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Sind(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Sind('0.51')
        ereal('5.3518479027559984754E-1')





Inverse sine, input in degrees, `\mathrm{asind}(x)`
-------------------------------------------------------------------------------

.. method:: math53.asind(x)

    where ``ctx`` is ``math53``, ``mathc53``, ``ctxcpp``, ``ctxflint``.

    Returns the inverse sine of `x`, `\mathrm{asin}(x)`. See also  Wikipedia :cite:p:`WikipediaFun50`,  MathWorld :cite:p:`WolframFun51`,  NIST :cite:p:`DLMFun50`, :cite:t:`Ehrhardt2018` (4.2.13), Mpmath :cite:p:`MpmathFun51`.




Cosine, `x` in degrees, `\mathrm{cosd}(x)`
-------------------------------------------------------------------------------

.. method:: math53.cosd(x)

    Returns the cosine of `x`, with `x` in degrees, `\mathrm{cosd}(x)`.   See also  Wikipedia :cite:p:`WikipediaFun30`,  MathWorld :cite:p:`WolframFun32`,  NIST :cite:p:`DLMFun30`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Cosd(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Cosd('0.51')
        ereal('5.3518479027559984754E-1')





Inverse cosine, input in degrees, `\mathrm{acosd}(x)`
-------------------------------------------------------------------------------

.. method:: math53.acosd(x)

    where ``ctx`` is ``math53``, ``mathc53``, ``ctxcpp``, ``ctxflint``.

    Returns the inverse cosine of `x`, `\mathrm{acos}(x)`. See also  Wikipedia :cite:p:`WikipediaFun50`,  MathWorld :cite:p:`WolframFun52`,  NIST :cite:p:`DLMFun50`, :cite:t:`Ehrhardt2018` (4.2.3), Flint :cite:p:`FlintFun50`, Flint :cite:p:`FlintFun51`, Mpmath :cite:p:`MpmathFun52`.





Tangent, with `x` in degrees, `\mathrm{tand}(x)`
-------------------------------------------------------------------------------

.. method:: math53.tand(x)

    Returns the tangent of `x`, with `x` in degrees, `\mathrm{tand}tan(x)`.  See also  Wikipedia :cite:p:`WikipediaFun30`,  MathWorld :cite:p:`WolframFun33`,  NIST :cite:p:`DLMFun30`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Tand(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Tand('0.51')
        ereal('5.3518479027559984754E-1')





Inverse tangent, input in degrees, `\mathrm{atand}(x)`
-------------------------------------------------------------------------------

.. method:: math53.atand(x)

    where ``ctx`` is ``math53``, ``mathc53``, ``ctxcpp`` or ``ctxflint``.

    Returns the inverse tangent of `x`, `\mathrm{atan}(x)`. See also  Wikipedia :cite:p:`WikipediaFun50`,  MathWorld :cite:p:`WolframFun53`,  NIST :cite:p:`DLMFun50`, :cite:t:`Ehrhardt2018` (4.2.15), Flint :cite:p:`FlintFun50`, Flint :cite:p:`FlintFun51`, Mpmath :cite:p:`MpmathFun53`.










Cotangent, with `x` in degrees, `\mathrm{cotd}(x)`
-------------------------------------------------------------------------------

.. method:: math53.cotd(x)

    Returns the cotangent of `x`, with `x` in degrees, `\mathrm{cotd}(x)`. See also  Wikipedia :cite:p:`WikipediaFun30`,  MathWorld :cite:p:`WolframFun36`,  NIST :cite:p:`DLMFun30`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Cotd(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Cotd('0.51')
        ereal('5.3518479027559984754E-1')







Inverse cotangent, input in degrees, `\mathrm{acotd}(x)`
-------------------------------------------------------------------------------

.. method:: math53.acotd(x)


    Returns the inverse cotangent of `x`, `\mathrm{acot}(x)`. See also  Wikipedia :cite:p:`WikipediaFun50`,  MathWorld :cite:p:`WolframFun56`,  NIST :cite:p:`DLMFun50`, :cite:t:`Ehrhardt2018` (4.2.5).








Auxiliary function,  `\mathrm{acos}(1-x)`
-------------------------------------------------------------------------------

.. method:: math53.acos1m(x)

    Returns `\mathrm{acos}(1-x)`, `0 \le x \le 2`, accurate also for `x` near 0.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Acos1m(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Acos1m('0.51')
        ereal('5.3518479027559984754E-1')









Haversine function `\mathrm{hav}(x) = (1 - \cos(x))/2`
-------------------------------------------------------------------------------

.. method:: math53.hav(x)

    Returns the haversine function `\mathrm{hav}(x) = (1 - \cos(x))/2 = \sin^2(x/2)`. See also  MathWorld :cite:p:`WolframFun302`,  Wikipedia :cite:p:`WikipediaFun302`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Haversine(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Haversine('0.51')
        ereal('5.3518479027559984754E-1')






Inverse haversine function `\mathrm{archav}(x) = \mathrm{acos}(1-2x)`
-------------------------------------------------------------------------------

.. method:: math53.archav(z)

    Returns the inverse haversine function `\mathrm{archav}(x) = \mathrm{acos}(1-2x) =2 \mathrm{asin}(\sqrt{x})`, `0 \le x \le 1`. See also  MathWorld :cite:p:`WolframFun303`,  Wikipedia :cite:p:`WikipediaFun303`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.ArcHaversine(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.ArcHaversine('0.51')
        ereal('5.3518479027559984754E-1')







Versine function `\mathrm{vers}(x) = 1 - \cos(x)`
-------------------------------------------------------------------------------

.. method:: math53.vers(x)

    Returns the versine function `\mathrm{vers}(x) = 1 - \cos(x)`.

    See also:   https://en.wikipedia.org/wiki/Versine#Haversine


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Versine(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Versine('0.51')
        ereal('5.3518479027559984754E-1')





Coversine, `\mathrm{covers}(x) = 1 - \sin(x)`
-------------------------------------------------------------------------------

.. method:: math53.covers(x)

    Returns the `\mathrm{covers}(x) = 1 - \sin(x)`.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Covers(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Covers('0.51')
        ereal('5.3518479027559984754E-1')







Versint function `\mathrm{versint}(x) = x - \sin(x)`
-------------------------------------------------------------------------------

.. method:: math53.versint (x)

    Returns `\displaystyle \mathrm{versint}(x) = \int_0^x \mathrm{vers}(t) \mathrm{d}t = x - \sin(x)`, accurate also near 0.


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.Versint(0.5)
        ereal('5.2359877559829887307E-1')
        >>> ereal.Versint('0.51')
        ereal('5.3518479027559984754E-1')










Integral of cos powers, `\mathrm{cosint}(n,x)`
-------------------------------------------------------------------------------

.. method:: math53.cosint(n,x)

    Returns `\displaystyle \mathrm{IC}_n(x) = \int_0^x \cos^n(t) \, \mathrm{d}t`, the integral of the nth cos power, for `n \ge 0`.

    See also  :cite:t:`Ehrhardt2018` (3.10.13).


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.CosInt(3, 4)
        ereal('5.2359877559829887307E-1')
        >>> ereal.CosInt(3, 12)
        ereal('5.3518479027559984754E-1')







Integral of sin powers, `\mathrm{sinint}(n,x)`
-------------------------------------------------------------------------------

.. method:: math53.sinint(n,x)

    Returns sinint(n,x) = integral(sin(t)^n, t=0..x), n >= 0

    Returns `\displaystyle \mathrm{IS}_n(x) = \int_0^x \sin^n(t) \, \mathrm{d}t`, the integral of the nth sin power, for `n \ge 0`.

    See also  :cite:t:`Ehrhardt2018` (3.10.14).


    An example in Python

    .. code-block:: pycon

        >>> from xlcalcnet import ereal
        >>> ereal.SinInt(3, 4)
        ereal('5.2359877559829887307E-1')
        >>> ereal.SinInt(3, 12)
        ereal('5.3518479027559984754E-1')