In freespace, the Electric Field component of a traveling electromagnetic wave is:
$$\vec{E}(t,z) = 10^3 sin(\omega t - \beta z) \hat{y}~~~\text{[V/m]}$$
Since the wave propagation is in freespace, the wave impedance is:
$$\eta = 120 \pi~~\Omega$$
Further, the wave impedance can be calculated as the ratio of the Electric field Amplitude to the Magnetic field Amplitude, that is:
$$\eta = \frac{E_y}{H_x}$$
Now for the part I don't get... when they calcuate wave impledence... they put a negative sign on the magnetic field amplitude as follows:
$$\eta = \frac{E_y}{-H_x}$$
And thus, the magnetic field can be calculated from the electric field as follows:
$$H_x = \frac{E_y}{-\eta}$$
$$\vec{H} = - \frac{10^3}{120\pi}\sin(\omega t - \beta z) \hat{x}~~~\text{[A/m]}$$
My question is this:
How did they know to put a negative on the $H_y$ term given that $\vec{E}(t,z) = 10^3 sin(\omega t - \beta z) \hat{z}$?