Is there a better variant of the Auxiliary Angle Method?

Question

I'm currently learning the Auxiliary Angle Method. Is either the sine or cosine variant of the method preferable?

$R*\sin(\theta±\alpha)$

$R*\cos(\theta±\alpha)$

Answer 1

This link may be of some help.

The only difference is that for $R \cdot \sin (\theta \pm \alpha)$, where $R = \sqrt {x^2 + y^2}$, we would use $\alpha = \arctan \dfrac {b}{a},$ while with $R \cdot \cos (\theta \pm \alpha)$, we would use $\alpha = \arctan \dfrac {a}{b}$.