Is the Average Value of Cos^2 Indeed 1?

[71GA]

Hello!
I want to know if average value of cos^2 is indeed 1 ?

Thank you.

 

[edgepflow]

Use the integral definition of average value and integrate from 0 to 2 PI. See what you get.

 

[mathman]

cos² + sin² = 1, so its average = 1, and each term has the same average, so the average value of cos² is 1/2.

 

[edgepflow]

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."

 

[71GA]

thank you