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fix and improve trigonometric help files
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
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18
help/csc
18
help/csc
@@ -11,7 +11,7 @@ TYPES
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return real
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DESCRIPTION
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Calculate the cosecant of x to a multiple of eps, with error less
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Calculate the trigonometric cosecant of x to a multiple of eps, with error less
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in absolute value than .75 * eps.
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This function is equivalent to:
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@@ -19,6 +19,9 @@ DESCRIPTION
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csc(x) = 1 / sin(x)
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EXAMPLE
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; print csc(1/2), csc(5/7), csc(42/7)
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2.08582964293348818577 1.52653601091884339347 -3.57889954725440563736
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; print csc(1, 1e-5), csc(1, 1e-10), csc(1, 1e-15), csc(1, 1e-20)
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1.1884 1.1883951058 1.188395105778121 1.18839510577812121626
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@@ -26,11 +29,10 @@ EXAMPLE
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~0.09047318155450436310+~0.04120099965201690801i ~0.09047320975303232503+~0.04120098628887626238i
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; pi = pi(1e-20)
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; print csc(pi/6, 1e-10), csc(pi/3, 1e-10), csc(4*pi/3, 1e-10)
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2 1.1547005384 -1.1547005384
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; print csc(pi/6), csc(pi/2), csc(pi)
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2 1 378303066284076833726.92240766640467212978
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; print csc(1/2), csc(5/7), csc(42/7)
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2.08582964293348818577 1.52653601091884339347 -3.57889954725440563736
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; # NOTE: The huge value for csc(pi) is because pi, as calculated, is not exact.
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LIMITS
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0 < eps < 1
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@@ -42,8 +44,10 @@ LINK LIBRARY
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SEE ALSO
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sin, cos, tan, cot, sec
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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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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, ahacovercos
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epsilon
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## Copyright (C) 1999,2023 Landon Curt Noll
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