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Simple Trig Identity

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Simplify this expression:
    f(t) = sin([tex]\beta[/tex]t)*cos([tex]\beta[/tex]t)

    2. Relevant equations

    Identities

    3. The attempt at a solution

    I started out by doing sin([tex]\beta[/tex]t)*sin([tex]\beta[/tex]t+[tex]\pi[/tex]/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original formula which it should. Anyone have an idea? Just the start would be MUCH appreciated.
     
    Last edited: Sep 20, 2009
  2. jcsd
  3. Sep 20, 2009 #2
    You have f(x) but no x anywhere on the other side. What is the variable and what is constant?
     
  4. Sep 20, 2009 #3
    Sorry about that. It should be f(t).
     
  5. Sep 20, 2009 #4
    The first thing that came to mind was 2sinxcosx = sin2x
     
  6. Sep 20, 2009 #5
    Ahh! I think that is what I needed. If 2sin(x)cos(x)=sin(2x) then I can multiply both sides by 2 which gives 2f(t)=2sin([tex]\beta[/tex]t)cos([tex]\beta[/tex]t). After, just carry the 2 over so you get f(t)=(1/2)sin(2[tex]\beta[/tex]t). Thanks man!!
     
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