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 · In trigonometry, the coordinates on a unit circle are represented as (cos θ, sin θ), whereas in hyperbolic functions, the pair (cosh θ, sinh θ) represents points on the right half of an …

Jul 12, 2025 · Inverse hyperbolic functions are found by taking the inverse of the hyperbolic function, i.e. if y = sinh x then, x = sinh-1 (y) this represents the inverse hyperbolic sin function.

Since cosh x> 0, sinh x is increasing and hence injective, so sinh x has an inverse, \arcsinh x. Also, sinh x> 0 when x> 0, so cosh x is injective on [0, ∞) and has a (partial) inverse, \arccosh x. The other …

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 …

The sinh function is defined in terms of the exponential function, as $\sinh (x) = \frac {e^x - e^ {-x}} {2}$. This relationship shows that the sinh function can be expressed as the difference between two …

Elementary Functions Sinh [z] (4084 formulas) Primary definition (1 formula) Specific values (167 formulas) General characteristics (9 formulas) Series representations (63 formulas) Integral …

Sinh (pronounced as “shine”) represents the hyperbolic sine function. While the trigonometric function sine is defined as a circle, sinh is related to measurements from a hyperbola.

The graphs and properties such as domain, range and asymptotes of the 6 hyperbolic functions: sinh (x), cosh (x), tanh (x), coth (x), sech (x) and csch (x) are presented.