The least expensive way to get sin of two 3d vectors.

Hello.
What's the best, the least expensive, way to get the sine of two vectors?
Sorry for such basic question.

 

I don't know if this is the absolute cheapest way, but it's how I would do it:

Code (csharp):

1. // the dot product of two normalized vectors is the cosine of the angle between
2. float cosine = dot(normalize(vecA), normalize(vecB));
3.  
4. // sin²(x) + cos²(x) = 1.0, so sin(x) = √(1.0 - cos²(x))
5. float sine = sqrt(1 - (cosine * cosine));

 

Thank you.
I thought it was the fastest way too.