I just want to make clear of the definition of sinc(x). I know there is a normalized and unnormalized definition for the sinc function. If we have unnormalized sinc then we have: $$\sin(x)/x=\text{sinc}(x) \hspace{0.2in}\textbf{unnormalized sinc function}$$
And for the normalized sinc we have: $$\sin(\pi x)/\pi x = \text{sinc}(x) \hspace{0.2in}\textbf{normalized sinc function}$$
My question is: If we have something like: $\dfrac{\sin\left(\frac{200\pi x}{500}\right)}{200\pi x }$, if we divide and multiply the equation by $500$, will this convert to be: $500\,\text{sinc}(x)$? It just a tad bit confusing about what constants stay if inside the argument of the sine (if any).