In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit …

The two basic hyperbolic functions are sinh and cosh: sinh (x) = ex - e-x2. (pronounced shine or sinch). cosh (x) = ex + e-x2.

Nov 25, 2024 · Learn the different hyperbolic trigonometric functions, including sine, cosine, and tangent, with their formulas, examples, and diagrams. Also, learn their identities.

What is the Difference Between Hyperbolic Functions and Trigonometric Functions? The basic difference between trigonometric and hyperbolic functions is that trigonometric functions are defined …

A very important fact is that the hyperbolic trigonometric functions take area as their argument (called "the hyperbolic angle," but this is just a name and has nothing to do with angles), as depicted below. …

Dec 14, 2024 · Here we define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. These provide a unique bridge between two groups of …

Dec 3, 2025 · The hyperbolic tangent arises in the calculation of and rapidity of special relativity. All three appear in the Schwarzschild metric using external isotropic Kruskal coordinates in general …

Jul 12, 2025 · Hyperbolic Functions are similar to trigonometric functions but their graphs represent the rectangular hyperbola. These functions are defined using hyperbola instead of unit circles. …

Unlike the ordinary (\circular") trig functions, the hyperbolic trig functions don't oscillate. Rather, both grow like et=2 as t ! 1, and e t=2 as t ! 1 . Their integrals are just as easy. In fact, they're a …

Nov 3, 2025 · These functions are most conveniently defined in terms of the exponential function, with sinh z = 1/2 (ez − e−z) and cosh z = 1/2 (ez + e−z) and with the other hyperbolic trigonometric …