Parity of inverse trigonometric functions

[Jhenrique]

When I place the trigonometric functions in the "wolfram google", it informs the parity of the function, so,

sin(x), sinh(x) -> odd
cos(x), cosh(x) -> even
tan(x), tanh(x) -> odd
cot(x), coth(x) -> odd
sec(x), sech(x) -> even
csc(x), csch(x) -> odd

arcsin(x), arcsinh(x) -> odd
arccos(x), arccosh(x) -> ?
arctan(x), arctanh(x) -> odd
arccot(x), arccoth(x) -> odd
arcsec(x), arcsech(x) -> ?
arccsc(x), arccsch(x) -> odd

with base in this comparison above, is correct to attribute a parity for arccos(x), arccosh(x), arcsec(x) and arcsech(x) as being even?

 

[PeroK]

In order to have an inverse, a function must be 1-1, hence it's inverse is also 1-1. In general, therefore, an inverse function cannot be even.

To get the inverse of a trig function, the function is restricted to an interval where it is 1-1. For arcsin, this is [-π/2, π/2] and for cos [0, π] etc.