# What do you do if you have to evaluate arcsin2?

what do you do if you have to evaluate arcsin2?

## Answers and Replies

radou
Homework Helper
what do you do if you have to evaluate arcsin2?

Nothing, since 2 is not in the domain.

HallsofIvy
Science Advisor
Homework Helper
$-1\le sin(x) \le 1$

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

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

dextercioby
Science Advisor
Homework Helper
what do you do if you have to evaluate arcsin2?

It comes down to solving the equation

$$\sin x =2$$

which has no solution in $\mathbb{R}$, and in $\mathbb{C}$ has the solution

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

arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Perhaps get the series for it and sub in 2, see what happens :S

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