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 …

tanh (z) = -i tan (iz) coth (z) = i cot (iz)

Learn Hyperbolic Trig Identities and other Trigonometric Identities, Trigonometric functions, and much more for free. Download Hyperbolic Trig Worksheets.

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

Identities. sinh(−x) = −sinh(x) cosh(−x) = cosh(x) And. tanh(−x) = −tanh(x) coth(−x) = −coth(x) sech(−x) = sech(x) csch(−x) = −csch(x) Odd and Even. Both cosh and sech are Even …

Jul 28, 2023 · Another useful identity is the hyperbolic addition formula for the hyperbolic tangent: tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x)*tanh(y)). This formula allows us to express the …

From these definitions, the following hyperbolic trigonometric identities can be derived which are strikingly similar to the standard trigonometric identites: \(\cosh x = \cosh (-x)\) \(\sinh x = - …

Jan 3, 2025 · Hyperbolic identities involving tanhx exist. They are not normally used as it is easier to use sinhx, coshx and their definitions. If you do use tanhx identities, be careful with implied …

Mathematics reference: Trigonometric identities-- PREVIOUS Various identities and properties essential in trigonometry.

Jul 8, 2023 · Hyperbolic trigonometric identities are mathematical relationships that involve hyperbolic functions, such as hyperbolic sine (sinh), hyperbolic cosine (cosh), and hyperbolic …