In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, hyperbolic functions are analogs of the ordinary trigonometric

Trigonometric function

In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...

, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" (icon or ˈ), and the hyperbolic cosine "cosh" (icon), from which are derived the hyperbolic tangent "tanh" (icon or , and so on, corresponding to the derived trigonometric functions. The inverse hyperbolic function

Inverse hyperbolic function

The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they give the area of a sector of the unit hyperbola in the same way that the inverse trigonometric functions give the arc length of a sector on the unit circle...

s are the area hyperbolic sine "arsinh" (also called "asinh" or sometimes "arcsinh") and so on.

Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola

Hyperbola

In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

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