Although I knew about the formula of $\sin(a+b)$, its various derivations (including that by $e^{i\theta}$), phasors, etc, but after two years I realised (while doing wave optics) that the formula for $\sin(a+b)$ can be written as follows:
\begin{align*} R\sin(\omega t+\delta)&=R\sin\omega t \cos \delta+R\cos\omega t \sin\delta \\&= (R\cos\delta)\sin\omega t + (R\sin\delta)\cos\omega t \\&= R_x\sin \omega t +R_y\cos\omega t \end{align*}
where $R_x=\cos \delta$ and $R_y=\sin \delta$. That seems to imply that $R\sin(\omega t+\delta)$ somehow means the x component in y direction + y component in x direction. (In case of cos, it is x component in x direction + y component in y direction). What is the geometric interpretation of this in terms of phasors?
I tried to draw some diagrams where an angle is being added to a phasor but got confused about what should the $\sin \omega t$ "direction" represent in the diagram.