Spherical Law of Cosines

Theorem
Let $\triangle ABC$ be a spherical triangle on the surface of a sphere whose center is $O$.

Let the sides $a, b, c$ of $\triangle ABC$ be measured by the angles subtended at $O$, where $a, b, c$ are opposite $A, B, C$ respectively.

Then:


 * $\cos a = \cos b \cos c + \sin b \sin c \cos A$

Also known as
Some sources refer to this result as just the cosine-formula.

Also see

 * Spherical Law of Sines


 * Law of Cosines
 * Law of Sines