Hyperbolic Sine (sinh)

The hyperbolic sine function, denoted as sinh(x), is one of the basic hyperbolic functions. It is defined as the difference of the exponential function e^x and its inverse e^-x, divided by two. Here, e represents the mathematical constant approximately equal to 2.718281828459. Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions, but defined for a hyperbola rather than a circle.

Hyperbolic functions arise in the solutions of certain linear differential equations, for example, the equation defining the shape of a hanging cable or chain, known as a catenary, the equations of heat transfer, and special relativity that describe hyperbolic rotations in Minkowski space.