sinhx=ex−e−x2\sinh x=\frac{e^x-e^{-x}}2sinhx=2ex−e−x, coshx=ex+e−x2\cosh x=\frac{e^x+e^{-x}}2coshx=2ex+e−x, tanhx=sinhxcoshx\tanh x=\frac{\sinh x}{\cosh x}tanhx=coshxsinhx. They obey identities like trig ones (cosh2x−sinh2x=1\cosh^2x-\sinh^2x=1cosh2x−sinh2x=1), and their inverses are logarithms, e.g. arsinhx=ln(x+x2+1)\operatorname{arsinh}x=\ln\left(x+\sqrt{x^2+1}\right)arsinhx=ln(x+x2+1).