The values of E^{2} and B^{2 }vary from point to point and from moment to moment. Hence, the effective values of E^{2} and B^{2} are their time averages.

The graph of sin^{2}θ and cos^{2}θ are identical in shape but shifted by π/2, so the average values of sin^{2}θ and Cos^{2}θ are also equal over any integral multiple of π.

and also sin^{2}θ + cos^{2}θ =1

So by symmetry the average of sin^{2}θ = average of cos^{2}θ =1/2