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
96 lines
3.2 KiB
Plaintext
96 lines
3.2 KiB
Plaintext
NAME
|
|
ahacoversin - inverse half coversed trigonometric sine
|
|
|
|
SYNOPSIS
|
|
ahacoversin(x [,eps])
|
|
|
|
TYPES
|
|
x number (real or complex)
|
|
eps 0 < real < 1, defaults to epsilon()
|
|
|
|
return number
|
|
|
|
DESCRIPTION
|
|
Calculate the inverse half coversed trigonometric sine of x to a multiple of eps with error less in
|
|
absolute value than .75 * eps.
|
|
|
|
This function is sometimes called ahacovers, or ahacvs, or archacoversin, is equivalent to:
|
|
|
|
ahacoversin(x) = asin(1 - 2*x)
|
|
|
|
EXAMPLE
|
|
; print ahacoversin(0), ahacoversin(0.5), ahacoversin(1)
|
|
1.57079632679489661923 0 -1.57079632679489661923
|
|
|
|
; print ahacoversin(-0.5), ahacoversin(-1)
|
|
1.57079632679489661923-1.31695789692481670863i 1.57079632679489661923-1.76274717403908605046i
|
|
|
|
; print ahacoversin(.5, 1e-5), ahacoversin(.5, 1e-10), ahacoversin(.5, 1e-15), ahacoversin(.5, 1e-20)
|
|
0 0 0 0
|
|
|
|
; print ahacoversin(5), ahacoversin(5i)
|
|
-1.57079632679489661923+2.88727095035762068505i 0.09918204387849273625-3.00312524371312921749i
|
|
|
|
; print ahacoversin(5+5i)
|
|
-0.73144212314418701068-3.29254348147605425075i
|
|
|
|
; pi = pi(1e-20)
|
|
; print ahacoversin(pi/6), ahacoversin(pi/3)
|
|
-0.04721509173238348552 -1.57079632679489661923+0.4311526751624601302i
|
|
|
|
; print ahacoversin(4*pi/3)
|
|
-1.57079632679489661923+2.6869677693029370051i
|
|
|
|
LIMITS
|
|
0 < eps < 1
|
|
|
|
LINK LIBRARY
|
|
NUMBER *qahacoversin(NUMBER *x, NUMBER *eps)
|
|
COMPLEX *c_ahacoversin(COMPLEX *x, NUMBER *eps)
|
|
|
|
SEE ALSO
|
|
sin, cos, tan, cot, sec, csc
|
|
asin, acos, atan, acot, asec, acsc
|
|
versin, coversin, vercos, covercos
|
|
aversin, acoversin, avercos, acovercos
|
|
haversin, hacoversin, havercos, hacovercos
|
|
ahaversin, 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: 2023/09/24 11:17:28
|
|
## 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/
|