NAME
    versin - versed trigonometric sine

SYNOPSIS
    versin(x [,eps])

TYPES
    x		number (real or complex)
    eps		0 < real < 1, defaults to epsilon()

    return	number

DESCRIPTION
    Calculate the versed trigonometric sine of x to a multiple of eps with error less in
    absolute value than .75 * eps.

    This function is sometimes called vers, is equivalent to:

	versin(x) = 1 - cos(x)

EXAMPLE
    ; print versin(1/2), versin(5/7), versin(42/7)
    0.12241743810962728388 0.24443865329930340153 0.03982971334963397945

    ; print versin(1, 1e-5), versin(1, 1e-10), versin(1, 1e-15), versin(1, 1e-20)
    0.4597 0.4596976941 0.45969769413186 0.4596976941318602826

    ; print versin(2 + 3i, 1e-5), versin(2 + 3i, 1e-10)
    5.18963+9.10923i 5.189625691+9.1092278938i

    ; pi = pi(1e-20)
    ; print versin(pi/6), versin(pi/2), versin(pi)
    0.13397459621556135324 1 2

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qversin(NUMBER *x, NUMBER *eps)
    COMPLEX *c_versin(COMPLEX *x, NUMBER *eps)

SEE ALSO
    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    coversin, vercos, covercos
    aversin, acoversin, avercos, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, hacoversin, havercos, ahacovercos
    epsilon

## Copyright (C) 2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:	2023/08/31 23:05:28
## File existed as early as:	2023
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/