# Time average of $\cos^2 x$ function [closed]

How do I find the time average of $\cos^2(3-wt)$ ?

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## closed as too localized by Lord_Farin, Michael Albanese, 23rd, TMM, Davide GiraudoApr 26 '13 at 12:58

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What is the definition of time average, and is "w" a constant? – dezign Apr 26 '13 at 11:39
What is the definition of time average of a function? And have you seen trigonometric identities such as $2\cos^2x= 1+\cos 2x$? – Dilip Sarwate Apr 26 '13 at 11:39

For a one variable function $f(t)$ with period $T$ the time average function is defined as

$$\frac{1}{T} \int_{0}^{T} dt f(t)$$

so what you need to compute is the following integral

$$\frac{1}{T}\int_{0}^{T}dt\cos^2(3-\omega t)$$

where $T$ is the smallest strictly positive number such that:

$$f(t+T)=f(t)$$

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Important: T is the smallest strictly positive number verifying $f(t+T)=f(t)$! – moray95 Apr 26 '13 at 11:59
@moray95 thank you – Jorge Apr 26 '13 at 12:02