Is the Average Value of Cos^2 Indeed 1?

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The average value of cos^2 over the interval from 0 to 2π is not 1, but rather 1/2, as derived from the integral definition of average value. This is supported by the identity cos^2 + sin^2 = 1, which indicates that both terms have equal averages. The discussion references a common teaching point from a physics class, emphasizing that the average value of the cosine squared function over a closed path is consistently stated as 1/2. Therefore, the assertion that the average value of cos^2 is 1 is incorrect. Understanding this concept is essential for accurate mathematical and physical analysis.
71GA
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Hello!
I want to know if average value of cos^2 is indeed 1 ?

Thank you.
 
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Use the integral definition of average value and integrate from 0 to 2 PI. See what you get.
 
cos2 + sin2 = 1, so its average = 1, and each term has the same average, so the average value of cos2 is 1/2.
 
I will never forget sitting in sophomore physics class in college and the Professor always said "the average value of the cosine squared function over a closed path is 1/2."
 
thank you
 

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