The hyperbolic sine, denoted as sinh, is a mathematical function that describes the relationship between the angles of a hyperbola, similar to how the regular sine function relates to a circle. It is defined as the difference between the exponential function and its inverse: sinh(x) = (e^x - e^(-x)) / 2, where e is the base of natural logarithms. This function is commonly used in various fields, including physics, engineering, and mathematics, particularly in problems involving hyperbolic geometry and wave equations. The graph of sinh resembles that of the regular sine function but extends infinitely in both directions, reflecting its exponential growth.