Fwd: Re: hyperbolic functions - set angle degrees

[Hans-Bernhard B. <HBB...@t-...>]

Oops, forgot to CC the list...

On 16.07.2012 22:39, Ethan A Merritt wrote:
> On Monday, July 16, 2012 12:39:28 pm Bastian Märkisch wrote:

>> While looking into the complex hyperbolic functions, I noticed that
>> asinh, acosh and atanh honour 'set angle degree' setting, while
>> sinh, cosh and tanh do not.
[...]
> I think that is because their domain is not "angles" but instead
> "hyperbolic angles". See
> http://en.wikipedia.org/wiki/Hyperbolic_angle

Obviously true for the real part of the argument of a hyperbolic
function --- not so much for the imaginary.

As-is, we break the defining identity sinh(asinh(x)) = x in 'set angles
degrees' mode.  That's seriously bad news, even if it's documented.
But if we remove the effect of this setting from asinh() etc., we break
another identity: asinh(i*x)=i * asin(x).  That's bad, too, in a
different way.

What this means that no matter what we do, something would break.  Might
as well leave it as it is, if only because people might be relying on
this status quo.

The only sane way out would be to remove 'set angles' altogether, but
I'm afraid it's about 20 years too late for that.