Direction of propagation of an EM wave

I'm reading my course book on ELectromagnetism and it is talking about a wave moving in the y-z plane but with polarisation in the x-direction, and it says that the equation

$$\mathbf{E}=E_0 2i sin(k_0 z\ cos \theta) exp[i(k_0 y\ sin \theta - \omega t)]\mathbf{e}_x$$

Shows that there is no propagation in the z-direction, but that instead a standing wave is formed when he wave bounces at an oblique angle between the two perfect conductors at z=0 and z=-a.

My question is...if the wave equation contains a factor involving z, how is it not propagating in the z direction? I suspect there is something I haven't understood about wave propagation and movement.

Thanks in advance