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https://github.com/lcn2/calc.git
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2c4abcd2b7
Added the following new trigonometric functions:
cas(x [,eps]) trigonometric cosine plus sine
cis(x [,eps]) Euler's formula
96 lines
3.2 KiB
Plaintext
96 lines
3.2 KiB
Plaintext
NAME
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ahacovercos - inverse half coversed trigonometric cosine
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SYNOPSIS
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ahacovercos(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 number
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DESCRIPTION
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Calculate the inverse half coversed trigonometric cosine 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 ahacvc, or archacovercos, or archacovercosine, is equivalent to:
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ahacovercos(x) = asin(2*x - 1)
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EXAMPLE
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; print ahacovercos(0), ahacovercos(0.5), ahacovercos(1)
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-1.57079632679489661923 0 1.57079632679489661923
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; print ahacovercos(-0.5), ahacovercos(-1)
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-1.57079632679489661923+1.31695789692481670863i -1.57079632679489661923+1.76274717403908605045i
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; print ahacovercos(.5, 1e-5), ahacovercos(.5, 1e-10), ahacovercos(.5, 1e-15), ahacovercos(.5, 1e-20)
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0 0 0 0
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; print ahacovercos(5), ahacovercos(5i)
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1.57079632679489661923-2.88727095035762068499i -0.09918204387849273625+3.00312524371312921749i
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; print ahacovercos(5+5i)
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0.73144212314418701068+3.29254348147605425075i
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; pi = pi(1e-20)
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; print ahacovercos(pi/6), ahacovercos(pi/3)
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0.04721509173238348552 1.57079632679489661923-0.4311526751624601302i
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; print ahacovercos(4*pi/3)
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1.57079632679489661923-2.68696776930293700505i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qahacovercos(NUMBER *x, NUMBER *eps)
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COMPLEX *c_ahacovercos(COMPLEX *x, NUMBER *eps)
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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
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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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: 2023/09/24 11:16:08
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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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