## gnuplot-beta

 hyperbolic functions - set angle degrees From: Bastian Märkisch - 2012-07-16 19:39:35 ```
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.

Bastian

```
 Re: hyperbolic functions - set angle degrees From: Ethan A Merritt - 2012-07-16 20:39:52 ```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. Ethan ```
 Re: hyperbolic functions - set angle degrees From: Bastian Märkisch - 2012-07-16 21:06:55 ```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 ```