There are many cases where you will want to find the time average of the square of a sinusoidal (or cosinusoidal) wave. An example would be calculating the average energy in the wave. Suppose I have two waves: E1 = Acos(kx − ωt + φ) E2 = B cos(kx − ωt + θ) where A and B (both real) are the amplitudes and φ and θ are the phases of the waves. They have the same wave vector k and angular frequency ω. (Assume the field directions are the same too.) 1 a. Calculate the time average of the product of E1 with E2 which is defined as E1E2 = 1 T T 0 E1E2 dt where T is a time interval long compared to the period of the wave.