Main Question or Discussion Point
Where do the definitions of hyperbolic functions in terms of exponentials come from ?
The most "obvious" formula from the geometry of a hyperbola would be cosh^2 x = sinh^2 x + 1.Thank you for that.
I wonder if the definitions in terms of exponentials can be gotten from the geometric definition. That would seem more natural than adding and subtracting trig functions with imaginary arguments.