File talk:Circular and hyperbolic angle.svg

The circle and hyperbola intersecting at (1,1) scales everything in the image by sqrt(2). Why not put the intersection point at (sqrt(2)/2,sqrt(2)/2) so that all of the cos/sin/cosh/sinh are times unit length? Or rather, why intersect with a circle of radius sqrt(2), when a circle of radius 1 would make things much more clearer?