Calculate electric field given the magnetic field

[whatisreality]

Homework Statement

The B field depends on z and t so that
$B = j B_{0}cos(kz-\omega t)$ where k is the wavenumber, $\omega$ is angular frequency and $B_{0}$ is constant.
The electric field is $E = E_{x}i + E_{y}j +E_{z}k$. Given $E_{y}=E_{z}=0$, and $E_{x}=\frac{\omega B_{0}}{k}$ at $t=z=0$, determine an expression for $E_{x}$.

Homework Equations

The Attempt at a Solution

I think I'm probably missing some sort of important concept! I feel like some sort of integration/differential equation should be involved, especially since $E_{x}$ at $t=z=0$ looks like a boundary condition. But I don't know how to turn this expression at t=0 into a general expression. It might not even have anything to do with the magnetic field...

 

[Simon Bridge]

You use your understanding of the relationship between E and B fields.
What sort of B field is the equation for?
What do you know about that kind of EM field?