Cosh, or hyperbolic cosine, is a mathematical function that is closely related to the more commonly known trigonometric functions, such as sine and cosine. It is defined as the ratio of the adjacent side of a right triangle to the hypotenuse, where the hypotenuse is the distance between the origin and a point on the hyperbola. Cosh has many applications in mathematics, physics, and engineering. For example, it is often used to model the shape of certain physical phenomena, such as the curve of a hanging chain or the shape of a catenary arch. It is also used in the study of differential equations and in the analysis of electric circuits, where it represents the voltage across a capacitor. Cosh is a smooth and continuous function with well-defined derivatives and integrals, and it has many important applications in mathematics, physics, engineering, finance, and economics.