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26fc394089
Improve builtin function strings, as printed by help builtin,
that use an optional accuracy (epsilon) arg by adding a comma.
Added the following new trigonometric functions:
crd(x [,eps]) trigonometric chord of a unit circle
acrd(x [,eps]) inverse trigonometric chord of a unit circle
95 lines
3.0 KiB
Plaintext
95 lines
3.0 KiB
Plaintext
NAME
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aexsec - inverse exterior trigonometric secant
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SYNOPSIS
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aexsec(x [,eps])
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TYPES
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x number (real or complex)
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eps 0 < real < 1, defaults to epsilon()
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return real
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DESCRIPTION
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Returns the inverse trigonometric secant of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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This function is sometimes called arcexsec, is equivalent to:
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aexsec(x) = asec(x + 1)
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EXAMPLE
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; print aexsec(0), aexsec(0.5), aexsec(1)
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0 0.84106867056793025578 1.04719755119659774615
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; print aexsec(-0.5), aexsec(-1)
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1.31695789692481670863i Error 10453
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; print aexsec(.5, 1e-5), aexsec(.5, 1e-10), aexsec(.5, 1e-15), aexsec(.5, 1e-20)
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0.84107 0.8410686706 0.84106867056793 0.84106867056793025578
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; print aexsec(5), aexsec(5i)
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1.40334824757520728868 1.53301882512452250055+0.1912765007419179263i
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; print aexsec(5+5i)
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1.4726099272282164647+0.08227107131216428876i
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; pi = pi(1e-20)
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; print aexsec(pi/6), aexsec(pi/3)
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0.85483795676480051293 1.06045782591172048268
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; print aexsec(4*pi/3)
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1.37685975548487957341
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qaexsec(NUMBER *x, NUMBER *eps)
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COMPLEX *c_aexsec(COMPLEX *c, NUMBER *epsilon)
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SEE ALSO
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sin, cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, excsc, aexcsc
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crd, acrd
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epsilon
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EXTERNAL RESOURCES
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For general information on trigonometric functions, see:
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https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
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https://en.wikipedia.org/wiki/Versine
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https://en.wikipedia.org/wiki/Exsecant
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https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
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https://en.wikipedia.org/wiki/Chord_(geometry)
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https://en.wikipedia.org/wiki/Secant_line
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https://en.wikipedia.org/wiki/Hartley_transform#cas
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https://en.wikipedia.org/wiki/Cis_(mathematics)
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## Copyright (C) 2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2023/10/01 00:20:20
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## File existed as early as: 2023
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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