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 …

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

Hyperbolic functions show up in many real-life situations. For example, they are related to the curve one traces out when chasing an object that is moving linearly.

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

Hyperbolic functions are defined analogously to trigonometric functions. We have main six hyperbolic functions, namely sinh x, cosh x, tanh x, coth x, sech x, and cosech x. They can be expressed as a …

We can similarly define functions on the unit hyperbola x 2 y 2 = 1, call x = cosh (t) the function hyperbolic cosine and y = sinh (t) the function hyperbolic sine.

Circular and hyperbolic functions. Definitions and identities. Derivatives of hyperbolic functions. Integrals of hyperbolic functions.

Mar 25, 2026 · The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and hyperbolic …

Certainly the hyperbolic functions do not closely resemble the trigonometric functions graphically. But they do have analogous properties, beginning with the following identity.

Jan 27, 2026 · Hyperbolic functions, the hyperbolic sine of z (written sinh z); the hyperbolic cosine of z (cosh z); the hyperbolic tangent of z (tanh z); and the hyperbolic cosecant, secant, and cotangent of z.