(a) In free space, find the electric field that corresponds to the time varying magnetic field
$$\overline{H}(y,t) = \hat{x} 10.0 \cos(3\pi \times 10^8 t - \pi y) \text{ A/m}$$
(b) In free space, find the magnetic field that corresponds to the time varying electric field
$$\overline{E}(x,t) = \hat{z} 5.0 \sin(4.5\pi \times 10^9 t + 15\pi x) \text{ V/m}$$