Finding the Sin of an Angle Between Two Vectors

[touqra]

For two arbitrary vectors, subtending an angle, $$\gamma$$, I know the cos relationship, but what's the sin relationship ? I ask because there is an ambiguity by only knowing the cosine form, since vector A can be either above or below vector B.

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

I don't know what's the correct term I should type in for search engine.

 

[mathman]

For two arbitrary vectors, subtending an angle, $$\gamma$$, I know the cos relationship, but what's the sin relationship ? I ask because there is an ambiguity by only knowing the cosine form, since vector A can be either above or below vector B.

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

I don't know what's the correct term I should type in for search engine.

It would clarify things if you could state what all these angles are and their relationships.