# Thread: Principle Value of Cosh

1. ## Principle Value of Cosh

The value of $arccosh$ is given as
$\ln {\color{red}(} x\pm\sqrt{x^2-1}{\color{red})}$,

but my book states that

$\ln {\color{red}(} x + \sqrt{x^2-1} {\color{red})}$

gives you the principle value. Is the principle value the positive one, the one we would normally take? I'm guessing you get this option due to the graph of $\cosh{x}$ being symmetrical about the y axis?

Thanks for clearing this one up.

2. I think it has sometihng to do with the graph of cosh always being positive.

Therefore only $ln(x+\sqrt{x^2-1})$ is the only one which is always positive.

3. Originally Posted by Showcase_22
I think it has sometihng to do with the graph of cosh always being positive.

Therefore only $ln(x+\sqrt{x^2-1})$ is the only one which is always positive.
A justification of this is required. A justification can be found here: http://www.math.cornell.edu/~kbrown/122/coshinv.pdf

4. Thanks, that worksheet explained it really well.