It is only about the hyperbolic versions; because there is no mathematical reason to call their inverse functions "arc". Maybe the mistake only happened because some of the hyperbolic functions start with a "c" (cosh, coth, csch) and then the inverse function somehow looks like having an "arc".

I think it would be consistent and in line with many textbooks (and wikipedia) if the display option would render inverse trigonometric functions with "arc" and inverse hyperbolic functions with "ar".

Stephan