Is this phase right?

Hello at physics lectures we wrote a phase of a sine wave like this:

$$\phi = kx - \omega t$$

Is this right? As I recall the phase of a wave should be written like this:

$$\phi = \omega t - kx$$

And if a wave changes direction $(k \rightarrow -k)$ like this:

$$\phi = \omega t + kx$$

Can someone explain to me if first usage is even possible and when if so.

-
The first two phases are the same, the sine only differs by an overall sign i.e. by normalization. The last formula only differs by its being a left-moving wave rather than a right-moving wave, i.e. by the sign of $k$. – Luboš Motl Sep 25 '12 at 12:16
Soo it holds that $\sin(x) = - \sin(-x)$ and therefore $\sin(\omega t - kx) = - \sin(kx - \omega t)$? – 71GA Sep 25 '12 at 19:00
Could you post your anwser below so i can give you points? – 71GA Oct 21 '12 at 7:07

It holds that $\sin(x) = - \sin(-x)$ and therefore $\sin(\omega t - kx) = - \sin(kx - \omega t)$.