Does anyone perhaps have a good way for me to get a lasting 'intuition' about what inverse hyperbolics are? I look at, for example, the well known sin x; it is periodic.

Then, it seems, sinh x is a reflection of sin x about the line y=x.

(I found an example at )

It ends up not very dissimilar from sin x , but with a limited range - it is not periodic?

Then arcsin x is again a reflection of sinh x about y=x. It looks closer to what sinx was , also not periodic?(example at )

But what do hyperbolic and inverse hyperbolic functions do - apart from causing me to see double after a while ....Sin is a wave, I can look at ripples in a pond etc. The others?