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

["David A. Wheeler" <dwheeler@dwheeler.com>]

Unsurprisingly, we have the trig functions:
 SIN COS TAN
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:
 http://www.gnome.org/projects/gnumeric/functions.shtml
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,
IMACSC and IMASEC.

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.

Thoughts?

--- David A. Wheeler