Why is the phase shift of a sin or cosine wave $c/b$? [closed]

I recognize this is a copy of Why is the phase shift -c/b instead of -c but I still don't understand. Plus that is five years old. Why is the phase shift of $y=\cos(2x-1)$ not one? Why is it $c/b$ or $1/2$?


Possibly helpful: Think of the phase shift as the value of $x$ that gives you an argument of $0$ in the sine or cosine function. So for $y=\cos(2x-1)$, we set $2x-1 \stackrel{\rm set}= 0$. This gives $x=\frac12$, corresponding to putting $0$ into the cosine function, for a phase shift of $\frac12$.