mirror of
https://github.com/lcn2/calc.git
synced 2025-08-16 01:03:29 +03:00
2c4abcd2b7
Added the following new trigonometric functions:
cas(x [,eps]) trigonometric cosine plus sine
cis(x [,eps]) Euler's formula
94 lines
3.1 KiB
Plaintext
94 lines
3.1 KiB
Plaintext
NAME
|
|
aversin - inverse versed trigonometric sine
|
|
|
|
SYNOPSIS
|
|
aversin(x [,eps])
|
|
|
|
TYPES
|
|
x number (real or complex)
|
|
eps 0 < real < 1, defaults to epsilon()
|
|
|
|
return real
|
|
|
|
DESCRIPTION
|
|
Returns the inverse versed trigonometric sine of x to a multiple of eps with error less in
|
|
absolute value than .75 * eps.
|
|
|
|
This function is sometimes called avers, or arcversin, is equivalent to:
|
|
|
|
aversin(x) = acos(1 - x)
|
|
|
|
EXAMPLE
|
|
; print aversin(0), aversin(0.5), aversin(1)
|
|
0 1.04719755119659774615 1.57079632679489661923
|
|
|
|
; print aversin(-0.5), aversin(-1)
|
|
0.96242365011920689498i 1.31695789692481670863i
|
|
|
|
; print aversin(.5, 1e-5), aversin(.5, 1e-10), aversin(.5, 1e-15), aversin(.5, 1e-20)
|
|
1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
|
|
|
|
; print aversin(5), aversin(5i)
|
|
3.14159265358979323846-2.06343706889556054673i 1.37700319023996442947+2.33097465304931241742i
|
|
|
|
; print aversin(5+5i)
|
|
2.23961290212082390892+2.55132162547569885882i
|
|
|
|
; pi = pi(1e-20)
|
|
; print aversin(pi/6), aversin(pi/3), aversin(4*pi/3)
|
|
1.07423928334711836378 1.61801141852728010475 3.14159265358979323846-1.82724307729474887791i
|
|
|
|
LIMITS
|
|
0 < eps < 1
|
|
|
|
LINK LIBRARY
|
|
NUMBER *qaversin_or_NULL(NUMBER *q, NUMBER *epsilon);
|
|
NUMBER *qaversin(NUMBER *q, NUMBER *epsilon);
|
|
COMPLEX *c_aversin(COMPLEX *c, NUMBER *epsilon);
|
|
|
|
SEE ALSO
|
|
sin, cos, tan, cot, sec, csc
|
|
asin, acos, atan, acot, asec, acsc
|
|
versin, coversin, vercos, covercos
|
|
acoversin, avercos, acovercos
|
|
haversin, hacoversin, havercos, hacovercos
|
|
ahaversin, hacoversin, havercos, ahacovercos
|
|
exsec, aexsec, excsc, aexcsc
|
|
crd, acrd
|
|
cas, cis
|
|
epsilon
|
|
|
|
EXTERNAL RESOURCES
|
|
For general information on trigonometric functions, see:
|
|
|
|
https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
|
|
https://en.wikipedia.org/wiki/Versine
|
|
https://en.wikipedia.org/wiki/Exsecant
|
|
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
|
|
https://en.wikipedia.org/wiki/Chord_(geometry)
|
|
https://en.wikipedia.org/wiki/Secant_line
|
|
https://en.wikipedia.org/wiki/Hartley_transform#cas
|
|
https://en.wikipedia.org/wiki/Cis_(mathematics)
|
|
|
|
## Copyright (C) 2023 Landon Curt Noll
|
|
##
|
|
## Calc is open software; you can redistribute it and/or modify it under
|
|
## the terms of the version 2.1 of the GNU Lesser General Public License
|
|
## as published by the Free Software Foundation.
|
|
##
|
|
## Calc is distributed in the hope that it will be useful, but WITHOUT
|
|
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
|
|
## Public License for more details.
|
|
##
|
|
## A copy of version 2.1 of the GNU Lesser General Public License is
|
|
## distributed with calc under the filename COPYING-LGPL. You should have
|
|
## received a copy with calc; if not, write to Free Software Foundation, Inc.
|
|
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
|
|
##
|
|
## Under source code control: 2023/09/03 00:26:24
|
|
## File existed as early as: 2023
|
|
##
|
|
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
|
|
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
|