It is often said that a hyperbolic angle is the area of the hyperbolic sector (the hyperbola being y=1/x) swept out by a ray drawn from the origin to the point (x, 1/x), where x>1. The starting line of the "sweep" is the ray y= x. And it is said that the hyperbolic angle is therefore equal to ln(x).
(For example here: Hyperbolic angle - Wikipedia, the free encyclopedia)
But then you also see that the hyperbolic angle is the hyperbolic sector (in this case the hyperbola being ) swept out by the ray drawn from the origin to the point . The starting ray of the sweep is the x axis in this case.
(For example here: Hyperbolic function - Wikipedia, the free encyclopedia)
How can be the area of both of these hyperbolic sectors, since an increase in one hyperbolic sector means the decrease of the other?
PS- I'm never sure where to put questions regarding hyperbolic functions. The calculus forum seems like a good place because hyperbolic functions are important for working through difficult integrals, as in my case.