# Hyperbolic trigonometry

From Encyclopedia of Mathematics

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:

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Hyperbolic_trigonometry&oldid=19080

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article