What is the average for cos2(x)?

[ucbugrad]

What is the expectation value of cosine squared, namely <cos^2(t)>?

 

[Tarantinism]

cos²x = (1+cos(2x))/2

Integration leads to 0,5 (averaged over the lenght)

 

[mathman]

Another approach: cos²(x) + sin²(x) = 1. Both terms have the same average, so the average for cos²(x) = 1/2.