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Subject: Missing trig functions: IMTAN, CSC, SEC. Add them?

Unsurprisingly, we have the trig functions:
We also have the cotangent, COT.

SIN and COS have imaginary versions IMSIN and IMCOS,
but there is no IMTAN nor IMCOT.  Gnumeric has these:
Including them would help interoperability with Gnumeric
spreadsheets, as well as improve application functionality.

Also, currently, we do not have the corresponding:
 CSC (cosecant)
 SEC (secant)

I propose that we add CSC and SEC, along with their
inverses ACSC and ASEC, and their
imaginary versions IMCSC and IMSEC.
We might also add the imaginary inverses,

I would put them all in the "large" group.

Then at least we would completely cover all the
"standard" normal trig functions shown in a typical
high school trig class.

We probably should do that for the hyperbolics, too:
CSCH - hyperbolic cosecant
SECH - hyperbolic secant
ACSCH - inverse hyperbolic cosecant
ASECH - inverse hyperbolic secant

Then we cover all the "usual" hyperbolic functions too.
(See http://en.wikipedia.org/wiki/Hyperbolic_function
for more on hyperbolic functions.)  Again, "large" group.

This would add several functions to the "large" group.
All are very well-known mathematical functions,
and numerical algorithm cookbook texts already cover them,
so I expect no difficulty defining them.
Gnumeric seems to implement some of these, esp. in
the imaginary group.

Note: Gnumeric uses the prefix "arc" instead of "A",
but since we name all other arc-functions beginning with
"A", I recommend that we stay consistent.  Gnumeric can
continue to present "arc.." names to users when displaying
in English, so this does not cause any hardship.


--- David A. Wheeler 

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