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Average Value of Sin^2(θ)

  • Thread starter gennarakis
  • Start date
  • #1
14
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How can <sin2θ>=1/2 and <cos2θ>=1/2

How is the proof made?Integrate sin2θ from -Infinity to +Infinity?
 

Answers and Replies

  • #2
berkeman
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How can <sin2θ>=1/2 and <cos2θ>=1/2

How is the proof made?Integrate sin2θ from -Infinity to +Infinity?
You only need to integrate over one cycle. Every other cycle will be the same, right?
 
  • #3
gb7nash
Homework Helper
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Average value on what interval?
 
  • #4
14
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I just integrated from 0 to 2Pi changed sin2θ=(1-cos2θ)/2 but the result is Pi and not 1/2...:confused:
 
  • #5
berkeman
Mentor
57,330
7,328
I just integrated from 0 to 2Pi changed sin2θ=(1-cos2θ)/2 but the result is Pi and not 1/2...:confused:
You forgot to divide by 2*PI to get the average over the interval...
 

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