Hyperbolic trigonometry

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The trigonometry on the Lobachevskii plane (cf. Lobachevskii geometry). Let , , be the lengths of the sides of a triangle on the Lobachevskii plane, and let be the angles of this triangle. The following relationship (the cosine theorem), which relates with , is valid:

All the remaining relations of hyperbolic trigonometry follow from this one, such as the so-called sine theorem:



[a1] H.S.M. Coxeter, "Non-Euclidean geometry" , Univ. Toronto Press (1965) pp. 224–240
[a2] H.S.M. Coxeter, "Angles and arcs in the hyperbolic plane" Math. Chronicle (New Zealand) , 9 (1980) pp. 17–33
How to Cite This Entry:
Hyperbolic trigonometry. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article