# Why use different arguments to plot a sine wave?

In my Electronics class were given some examples of sine wave graphs that represent voltage in respect to time, $v(t) = A \sin(\omega t)$ and other graphs whose $x$ axis is $\omega t$ instead of $t$, like in the image below:

I know the product $\omega t$ gives an angle, but I want to know what is the reason to use this notation instead of representing the sine wave with respect to time. Is there an advantage? Are there any examples in real life that explain the need of representing waves in this form?

With that kind of thinking, plotting a wave in terms of $\omega$ makes sense - it helps you focus on the elements of the wave that matter more. You end up plotting phase along the X axis so things like power reflection etc are immediately obvious.