Re: hyperbolic functions - set angle degrees

[Bastian M. <bma...@we...>]

Am 16.07.2012 22:39, schrieb Ethan A Merritt:
> 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 know this is documented (see 'help set angles'). But I am curious if anybody remembers the rationale behind this. Is it because of relations like asinh(x) = -i asin(i x)?
>>   I have also tried out various pocket calculators and a few calculator programs, but none of them considered the deg/rad setting for the (inverse) hyperbolic functions.
>>
>
> I think that is because their domain is not "angles" but instead "hyperbolic angles".
> See
> 	http://en.wikipedia.org/wiki/Hyperbolic_angle
>
> Under this interpretation the independent variable is not in radians to begin with,
> so converting it to degrees does not make sense.

That's what I thought. But why do asinh, acosh and atanh care about the 
setting? Should we change that?
Btw. my good old HP48G calculator also ignores the deg/rad setting for 
complex arguments to sin, cos and tan.

Bastian