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Need explanation about sin rule

  1. Jan 27, 2014 #1
    Hello.
    This is part of a solution but I don't understand the underlined part. Why is it equals to 0?
     

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  2. jcsd
  3. Jan 27, 2014 #2
    sin(wt)/6 x sin(2wt-(pi/4))
    is not equal to zero.
     
  4. Jan 29, 2014 #3

    NascentOxygen

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    Staff: Mentor

    That term itself isn't zero. But the area under it, taken over the complete cycle 0→2 Pi contributes nothing to the integral that you are about to evaluate. So the author is just looking ahead and seeing that he can save himself a bit of work here, and not bothering to process a term that is going to end up as zero anyway.

    Why don't you work through without dismissing that term, and see how the result pans out?
     
  5. Jan 29, 2014 #4

    D H

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    Staff Emeritus
    Science Advisor

    An easy way to show that that term integrates to zero is to use the identity ##\sin(a)\sin(b) = \frac 1 2 \bigl(\cos(a-b) - \cos(a+b)\bigr)##.
     
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