I have an definition that is calculating the angle between two vectors:
$\sin(\alpha) = -a \cdot b$
(the sign $\cdot$ stands for a dot product, and $a$ and $b$ are unit vectors).
I understand that the dot product when equal to cosine of an angle is just the angle between the two vectors, but what does it mean when the dot product is equal to the sine of an angle?
Here are the equations and a diagram for how the angle want to be computed as well as a link to the paper:
As the equation $\sin\alpha =-a\cdot b$ is equivalent to $\sin(-\alpha)=a\cdot b,$ or $$a\cdot b = \cos(π/2+\alpha),$$ it follows that the angle between the vectors cannot be $\alpha,$ but possibly $\alpha+π/2.$