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NAME
aexsec - inverse exterior trigonometric secant
SYNOPSIS
aexsec(x [,eps])
TYPES
x number (real or complex)
eps 0 < real < 1, defaults to epsilon()
return real
DESCRIPTION
Returns the inverse trigonometric secant of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called arcexsec, is equivalent to:
aexsec(x) = asec(x + 1)
EXAMPLE
; print aexsec(0), aexsec(0.5), aexsec(1)
0 0.84106867056793025578 1.04719755119659774615
; print aexsec(-0.5), aexsec(-1)
1.31695789692481670863i Error E_AEXSEC_3
; print aexsec(.5, 1e-5), aexsec(.5, 1e-10), aexsec(.5, 1e-15), aexsec(.5, 1e-20)
0.84107 0.8410686706 0.84106867056793 0.84106867056793025578
; print aexsec(5), aexsec(5i)
1.40334824757520728868 1.53301882512452250055+0.1912765007419179263i
; print aexsec(5+5i)
1.4726099272282164647+0.08227107131216428876i
; pi = pi(1e-20)
; print aexsec(pi/6), aexsec(pi/3)
0.85483795676480051293 1.06045782591172048268
; print aexsec(4*pi/3)
1.37685975548487957341
LIMITS
0 < eps < 1
LINK LIBRARY
NUMBER *qaexsec(NUMBER *x, NUMBER *eps)
COMPLEX *c_aexsec(COMPLEX *c, NUMBER *epsilon)
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec, acsc
versin, coversin, vercos, covercos
aversin, acoversin, avercos, acovercos
haversin, hacoversin, havercos, hacovercos
ahaversin, hacoversin, havercos, ahacovercos
exsec, excsc, aexcsc
crd, acrd
cas, cis
epsilon
EXTERNAL RESOURCES
For general information on trigonometric functions, see:
https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
https://en.wikipedia.org/wiki/Versine
https://en.wikipedia.org/wiki/Exsecant
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
https://en.wikipedia.org/wiki/Chord_(geometry)
https://en.wikipedia.org/wiki/Secant_line
https://en.wikipedia.org/wiki/Hartley_transform#cas
https://en.wikipedia.org/wiki/Cis_(mathematics)
## 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: 2023/10/01 00:20:20
## 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/
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