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fdbf53d7e8
Improved trig help files. Added new vercos(x, [,eps]) for versed cosine and covercos(x, [,eps]) for inverse versed cosine. Added new avercos(x, [,eps]) for inverse versed cosine and acovercos(x, [,eps]) for inverse coversed cosine.
64 lines
2.1 KiB
Plaintext
64 lines
2.1 KiB
Plaintext
NAME
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avercos - inverse versed trigonometric cosine
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SYNOPSIS
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avercos(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 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 averc, or arcvercos, is equivalent to:
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avercos(x) = acos(x - 1)
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EXAMPLE
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; print avercos(.5, 1e-5), avercos(.5, 1e-10), avercos(.5, 1e-15), avercos(.5, 1e-20)
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2.0944 2.0943951024 2.094395102393195 2.09439510239319549231
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; print avercos(2), avercos(-5), avercos(2 + 3i)
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0 3.14159265358979323846-2.47788873028847500481i 1.26319267726418536931-1.86416154415788242834i
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qavercos_or_NULL(NUMBER *q, NUMBER *epsilon);
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NUMBER *qavercos(NUMBER *q, NUMBER *epsilon);
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COMPLEX *c_avercos(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, avercos
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aversin, acoversin, covercos, acovercos
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epsilon
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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: 2023/09/05 23:40:24
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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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