Hi, I understand why Cosix=Coshx, using Eulers identity and thus proving the Hyperbolic exponential definitions of Sinh and Cosh using this. I do not understand how this relates to the graph of the Hyperbola. i.e. the hyperbolic functions come from the unit Hyperbola, but how can your prove from that the exponential definitions of Sinh and Cosh? I can see how the graphs of Sinh and Cosh come from the Hyperbola but then how was it known from that, that Sinhx =1/2(e^x-e^-x) ? All help appreciated!