For any triangle in the Euclidean plane with sides and opposite angles , respectively, the equalities
hold, where is the radius of the circumscribed circle.
In spherical geometry the sine theorem reads
and in Lobachevskii geometry:
|[a1]||H.S.M. Coxeter, S.L. Greitzer, "Geometry revisited" , Math. Assoc. Amer. (1975)|
Sine theorem. Yu.A. Gor'kov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sine_theorem&oldid=12252