hyperbolic function (redirected from Osborne's rule)

hyperbolic function

In mathematics, one of a set of functions related to the hyperbola in the same way the trigonometric functions relate to the circle. They are the hyperbolic sine, cosine, tangent, secant, cotangent, and cosecant (written “sinh,” “cosh,” etc.). The hyperbolic equivalent of the fundamental trigonometric identity is cosh²z − sinh²z = 1. The hyperbolic sine and cosine, particularly useful for finding special types of integrals, can be defined in terms of exponential functions:

sinhx = (e^x − e^−x) ÷ 2 and coshx = (e^x + e^−x) ÷ 2