The cosh function, short for hyperbolic cosine, is a mathematical function defined for real numbers. It is expressed as \cosh(x) = \frace^x + e^{-x}2, where e is the base of the natural logarithm. The cosh function is used in various fields, including engineering and physics, to model phenomena such as waveforms and the shape of hanging cables. The graph of the cosh function resembles a U-shape, always remaining above the x-axis. It is an even function, meaning that \cosh(-x) = \cosh(x). The cosh function is part of a family of hyperbolic functions, which also includes the sinh function and tanh function, and is closely related to trigonometric functions in the context of hyperbolic geometry.