File talk:Hyperbolic functions.svg

Just as an improvement the red lines presenting where the values for cosh and sinh are located are a bit missleading. I think that some people will interpret the red line to show the point on the axises' where that value is located. To show that it in fat means the distance on the paralel axis to the line curly-type indicators would be better i guess... Gillis (talk) 22:46, 23 January 2008 (UTC)

Interesting! I've always wanted to find a geometric description for that value. (JDoolin (talk) 21:49, 22 September 2010 (UTC))

I've been meaning to verify this, and I just tried in Mathematica:$$\int_{x=0}^{sinh(\theta)}\left (\sqrt{1+x^2}-\frac{x}{tanh(\theta)} \right )=\frac{\theta}{2}$$

Technically, it came out to be $$\frac{1}{2} \left(\sinh ^{-1}(\sinh (\theta ))+\sinh (\theta ) \left(\sqrt{\cosh ^2(\theta )}-\cosh (\theta )\right)\right)$$ ...which is the same thing. --JDoolin (talk) 21:42, 19 October 2010 (UTC)