Answer
(a) The wave is traveling in the -z-direction.
(b) We can write the components of the electric field of this wave:
$E_x = -(c~B_m)~cos~(kz+\omega~t)$
$E_y = 0$
$E_z = 0$
Work Step by Step
(a) From the term $kz+\omega~t$, we can see that the wave is traveling in the -z-direction.
(b) Since the direction of propagation is determined by the cross-product $E\times B$, by the right-hand rule, the electric field must be pointing in the -x-direction at z = 0 and t = 0. Note that $(-x)\times (+y) = -z$
We can write the components of the electric field of this wave:
$E_x = -(c~B_m)~cos~(kz+\omega~t)$
$E_y = 0$
$E_z = 0$
