The sinh function, short for hyperbolic sine, is a mathematical function defined as the difference between the exponential function and its inverse. It is expressed as \sinh(x) = \frace^x - e^{-x}2, where e is the base of natural logarithms. The function is useful in various fields, including engineering and physics, particularly in problems involving hyperbolic geometry. The sinh function is part of a family of hyperbolic functions, which also includes cosh (hyperbolic cosine) and tanh (hyperbolic tangent). These functions share properties similar to trigonometric functions but are based on hyperbolas instead of circles. The sinh function is odd, meaning \sinh(-x) = -\sinh(x), and it plays a significant role in calculus and differential equations.