Is the Average Value of Cos^2 Indeed 1?

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Discussion Overview

The discussion centers around the average value of the function cos²(x) over a specified interval, specifically questioning whether this average value is indeed 1. The scope includes mathematical reasoning and integration techniques.

Discussion Character

  • Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant suggests using the integral definition of average value and integrating from 0 to 2π to find the average.
  • Another participant states that since cos²(x) + sin²(x) = 1, the average value of cos²(x) must be 1/2, as each term has the same average.
  • A third participant recalls a professor stating that the average value of the cosine squared function over a closed path is 1/2.

Areas of Agreement / Disagreement

There is no consensus on the average value of cos²(x); participants present differing views on the calculation and interpretation of the average value.

Contextual Notes

The discussion involves assumptions about the interval of integration and the properties of trigonometric functions, which may not be fully explored or agreed upon.

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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