hyperbolic function

The hyperbolic sine is a hyperbolic function defined in terms of exponential functions, characterized by odd symmetry and closely related to the hyperbolic cosine.

The hyperbolic tangent is a hyperbolic function defined as the ratio of the hyperbolic sine to the hyperbolic cosine, with values ranging between $−1$ and $1$.

The hyperbolic cotangent function is the ratio of the hyperbolic cosine to the hyperbolic sine, defined for all nonzero real numbers.