1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Average integral

  1. Sep 15, 2015 #1
    • Member warned about posting with no effort
    1. The problem statement, all variables and given/known data

    Show that <sin^2(k*r-wt)>= 1/2
    2. Relevant equations
    <f(t)>= 1/T integral ( f(t')dt' ) from [t, t+T]

    3. The attempt at a solution
  2. jcsd
  3. Sep 15, 2015 #2


    User Avatar
    Science Advisor

    Trigonometric identities: You know that [itex]\cos(2x)=\cos^{2}(x)-\sin^{2}(x)=1-2\sin^{2}(x) [/itex]?
  4. Sep 15, 2015 #3
    Right, so I use the appropriate identity ( 1-2sin^2(x) ), and carry out the integration?
  5. Sep 15, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Try it and see!
  6. Sep 15, 2015 #5


    User Avatar
    Science Advisor

    Well, I do not know exactly what you mean, but solve the identity for sin2(x) and integrate (for example from 0 to 2π).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Time Average integral