What do you do if you have to evaluate arcsin2?

Nothing, since 2 is not in the domain.

 

[itex]-1\le sin(x) \le 1[/itex]

There is no x such that sin(x)= 2 and so arcsin 2 is not defined.

 

Perhaps get the series for it and sub in 2, see what happens :S

 

It comes down to solving the equation

[tex] \sin x =2 [/tex]

which has no solution in [itex] \mathbb{R} [/itex], and in [itex] \mathbb{C} [/itex] has the solution

[tex] x=-i\ln\left(2\pm i\sqrt{3}\right)+2k\pi \ , \forall k\in\mathbb{Z} [/tex]

 

Which would diverge.
A Pade approximant might give you some silly number, though.