Explanation on how to arrive at equation for EM wave?

[serverxeon]

It is known that the electric field component of the EM wave is given by
E=E_{0}cos(kx-\omega t)

How do I arrive at such a form?
It is quite different from the standard sinusoidal equation of y=Acos(\omega t+\varphi)

Any guidance?
What does the kx-\omega t describe physically?

 

[Dick]

It is known that the electric field component of the EM wave is given by
E=E_{0}cos(kx-\omega t)

How do I arrive at such a form?
It is quite different from the standard sinusoidal equation of y=Acos(\omega t+\varphi)

Any guidance?
What does the kx-\omega t describe physically?

Your 'standard form' describes a wave that is constant at all values of x and only varies with t. The given form describes a 'travelling wave' that varies not only with time but with space as well. It has a constant shape but moves at velocity ω/k.