# Why is Mathematica giving me fits when I try to evaluate ArcCosh[Sqrt[2]]?

1. Feb 19, 2009

### AxiomOfChoice

For some reason, Mathematica will not comply when I try to determine

$$\cosh^{-1}(\sqrt{2})$$

Why is this the case? Is $$\cosh^{-1}(x)$$ undefined there or something? If so, why? I don't really see it...

Thanks!

UPDATE: Looks like Maple 11 refuses to evaluate $$\cosh^{-1}(\sqrt{2})$$ too. What is going on here?!

Last edited: Feb 19, 2009
2. Feb 19, 2009

### mgb_phys

Don't know, have you tried ln(x+root(x^2-1)) instead?

3. Feb 19, 2009

### Gokul43201

Staff Emeritus
Last edited by a moderator: May 4, 2017
4. Feb 19, 2009

### CRGreathouse

http://www.research.att.com/~njas/sequences/A091648 [Broken]

Last edited by a moderator: May 4, 2017
5. Feb 19, 2009

### Phrak

It could be a problem if you have replaced this $\sqrt{2}$ with this $2^{1/2}$.

6. Feb 19, 2009

### Gokul43201

Staff Emeritus
If the OP is looking for a decimal approximation, then something along the lines of Round[ArcCosh[Sqrt[2]],0.0001] should work just as well on Mathematica.

Last edited by a moderator: May 4, 2017
7. Feb 19, 2009

### CRGreathouse

I thought the additional information there (inflection point, etc) might be relevant the the unstated underlying problem.

8. Feb 19, 2009

### uart

Hi AxiomOfChoice, what exactly do you mean by evaluate in this case? Maple will try to symbolically simply an expression, it wont return a decimal approximation unless you tell it to (typically using the "evalf" function.

I've got Maple 7 and "evalf(arccosh(sqrt(2)));" returns 0.8813735866.

Last edited: Feb 19, 2009