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2c4abcd2b7
Added the following new trigonometric functions:
cas(x [,eps]) trigonometric cosine plus sine
cis(x [,eps]) Euler's formula
97 lines
3.2 KiB
Plaintext
97 lines
3.2 KiB
Plaintext
NAME
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ahavercos - inverse half versed trigonometric cosine
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SYNOPSIS
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ahavercos(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 half versed 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 ahaverc, or archavercos, or archavercosine, is equivalent to:
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ahavercos(x) = acos(2*x - 1)
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EXAMPLE
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; print ahavercos(0), ahavercos(0.5), ahavercos(1)
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3.14159265358979323846 1.57079632679489661923 0
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; print ahavercos(-0.5), ahavercos(-1)
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3.14159265358979323846-1.31695789692481670863i 3.14159265358979323846-1.76274717403908605046i
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; print ahavercos(.5, 1e-5), ahavercos(.5, 1e-10), ahavercos(.5, 1e-15), ahavercos(.5, 1e-20)
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1.5708 1.5707963268 1.570796326794897 1.57079632679489661923
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; print ahavercos(5), ahavercos(5i)
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2.88727095035762068505i 1.66997837067338935548-3.00312524371312921749i
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; print ahavercos(5+5i)
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0.83935420365070960856-3.29254348147605425075i
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; pi = pi(1e-20)
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; print ahavercos(pi/6), ahavercos(pi/3)
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1.52358123506251313372 0.4311526751624601302i
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; print ahavercos(4*pi/3)
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2.6869677693029370051i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qahavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
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NUMBER *qahavercos(NUMBER *q, NUMBER *epsilon);
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COMPLEX *c_ahavercos(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, ahacovercos
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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 11:18:04
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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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