# What is the name of this formula?

There is 3d angle addition formula for which I would like to know what it is called in the literature:

Given two vectors $\vec v_1$, $\vec v_2$ at (physicist's) angles $(\theta_1,\,\phi_1)$ and $(\theta_2,\,\phi_2)$, the angle $\Theta$ between the two vectors is given by:

$$\cos \Theta=\cos \theta_1 \cos\theta_2+\sin\theta_1\sin\theta_2\cos(\phi_1-\phi_2)$$

What is the name of this formula?

• It looks an awful lot like the Spherical Law of Cosines. – Blue Jul 8 '13 at 15:18
• This is the name I was looking for! Thanks, Blue!! – QuantumDot Jul 12 '13 at 1:35

Apparently, my comment answered the question. I'll convert the comment to a formal answer in order to get the question out of the Unanswered queue.

The formula looks an awful lot like the Spherical Law of Cosines.

I do not know the name of the formula, but it is derived from the dot product in spherical coordinates. See this pdf: http://people.wku.edu/david.neal/117/Unit5/MoreSpherical.pdf