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fix and improve trigonometric help files

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The trigonometric file files have had several bug fixed.

The EXAMPLE sections of trigonometric file have
been made consistent.

Added these new help files in anticipation of
the code for these new (i.e., to be written) builtin functions:

    hacovercos hacoversin havercos haversin
    ahacovercos ahacoversin ahavercos ahaversin
This commit is contained in:
Landon Curt Noll
2023-09-24 12:52:14 -07:00
parent db80afb843
commit ab95e47c0a
30 changed files with 928 additions and 176 deletions
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40
help/acsc
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@@ -11,26 +11,36 @@ TYPES
return real
DESCRIPTION
Returns the inverse cosecant of x to a multiple of eps with error less in
Returns the inverse trigonometric cosecant of x to a multiple of eps with error less in
absolute value than .75 * eps.
This function is sometimes called arccsc, is such that:
csc(acsc(x)) = x
and such that:
acsc(x) = asin(1/x)
This function is sometimes called arccsc.
EXAMPLE
; print acsc(2, 1e-5), acsc(2, 1e-10), acsc(2, 1e-15), acsc(2, 1e-20)
0.5236 0.5235987756 0.523598775598299 0.52359877559829887308
; print acsc(0), acsc(0.5), acsc(1)
Error 10454 1.57079632679489661923-1.31695789692481670863i 1.57079632679489661923
; print acsc(-0.5), acsc(-1)
-1.57079632679489661923+1.31695789692481670863i -1.57079632679489661923
; print acsc(.5, 1e-5), acsc(.5, 1e-10), acsc(.5, 1e-15)
1.5708-1.31696i 1.5707963268-1.3169578969i 1.570796326794897-1.316957896924817i
; print acsc(.5, 1e-20)
1.57079632679489661923-1.31695789692481670863i
; print acsc(5), acsc(5i)
0.20135792079033079145 -0.19869011034924140648i
; print acos(5+5i)
0.79039774680951249644-2.64919617780647114961i
; print acsc(5+5i)
0.09966370285979516002-0.10033029811220500594i
; pi = pi(1e-20)
; print acsc(pi/6), acsc(pi/3)
1.57079632679489661923-1.26327680856656556834i 1.2694227170496051647
; print acsc(4*pi/3)
0.24106031273407362824
LIMITS
0 < eps < 1
@@ -42,8 +52,10 @@ LINK LIBRARY
SEE ALSO
sin, cos, tan, cot, sec, csc
asin, acos, atan, acot, asec
versin, coversin, vercos, avercos
aversin, acoversin, covercos, acovercos
versin, coversin, vercos, covercos
aversin, acoversin, avercos, acovercos
haversin, hacoversin, havercos, hacovercos
ahaversin, hacoversin, havercos, ahacovercos
epsilon
## Copyright (C) 1999,2021,2023 Landon Curt Noll