I’ve written before about the law of cosines on a sphere: cos(c) = cos(a) cos(b) + sin(a) sin(b) cos(C). But that’s just one of two laws of cosines on a sphere. The equation above is the law of cosines for sides. The law of cosines for angles is typographically very similar, just inverting the case of […] The post Duality in spherical trigonometry first appeared on John D. Cook.