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b0a48a2b70
Added new versin(x, [,eps]) for versed sine and vercos(x, [,eps]) for versed cosine. Updated trig help files.
68 lines
2.1 KiB
Plaintext
68 lines
2.1 KiB
Plaintext
NAME
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vercos - versed cosine
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SYNOPSIS
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vercos(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 versed 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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The versed cosine function is sometimes called coversin, sometimes called cvs,
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may be defined as:
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vercos(x) = 1 - sin(x)
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EXAMPLE
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; print vercos(0.2), vercos(3/7), vercos(-31)
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0.80133066920493878454 0.58442814500694799193 0.59596235467693499395
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; print vercos(1, 1e-5), vercos(1, 1e-10), vercos(1, 1e-15), vercos(1, 1e-20)
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0.15853 0.1585290152 0.158529015192104 0.15852901519210349335
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; print vercos(2 + 3i, 1e-5), vercos(2 + 3i, 1e-10)
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-8.1545+4.16891i -8.1544991469+4.16890696i
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; pi = pi(1e-20)
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; print vercos(pi/6, 1e-10), vercos(pi/2, 1e-10), vercos(pi, 1e-10), vercos(3*pi/2, 1e-10)
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0.5 0 1 2
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qvercos(NUMBER *x, NUMBER *eps)
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COMPLEX *c_vercos(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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sin, cos, tan, sec, csc, cot, epsilon
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versin
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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: 2023/08/31 23:07:08
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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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