ABSTRACT
Trigonometric functions are called 'circular functions' since they arise naturally in connection with the geometry of the circle. There are other functions which are associated with the geometry of the conic section called a hyperbola and are thus classified as hyperbolic functions. Such functions have several applications, in particular with transmission line theory and with catenary problems, a catenary being a curve formed by a chain or rope of uniform density hanging freely from two fixed points not in the same vertical line. Hyperbolic functions may be evaluated readily using a calculator. Some scientific notation calculators possess sinh, cosh and tanh functions, however, if a calculator does not have these functions then the hyperbolic functions are evaluated from their definitions. Osborne's rule states that the six trigonometrical ratios used in trigonometrical identities relating general angles may be replaced by their corresponding hyperbolic functions, but the sign of any direct or implied product of two sines must be changed.
