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Trigonometry Identity problem I been trying to solve all day

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data
    solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2pi


    2. Relevant equations



    3. The attempt at a solution
    3(cos(x) + 1) = 2 sin^2(x)
    3(cos(x) + 1) = 2 (1- cos^2(x))
    I've tried this variation, and a couple others but it just does not pan out. Please help.

    Oh yeah we have a real uninformative book.
     
  2. jcsd
  3. Apr 23, 2009 #2
    Don't factor out the 3 on the left side. Instead, distribute the right side, and move everything to the left side. After doing that, do you recognize the equation?


    01
     
  4. Apr 23, 2009 #3
    OK so I get the following
    3 cos(x) + 3 = 2 - 2 cos^2(x)
    3 cos(x) + 1 + 2 cos^2(x)=0
    I tried this variation before, but I was unsure of what to do with the 1+2 cos^2(x) part. or maybe i'm just doing something wrong with the distribution and movement of the right side.
     
  5. Apr 23, 2009 #4
    hold on I think I understand now.
    (3 cos(x)+1)(2cos^2(x))= 0, the solve those two for 0
     
  6. Apr 23, 2009 #5
    No no no, that's not right. It's best if you put the equation in "standard form" first, like this:
    2cos^2(x) + 3 cos(x) + 1 = 0
    Do you see what to do now?


    01
     
  7. Apr 23, 2009 #6
    wow. My head was so wrapped up in Identities I didn't even think to factor them in standard form
    (cos +1)(2cos+1)=0
    Thank you for shining a light through this fogged up brain of mine
     
  8. Apr 23, 2009 #7

    Mark44

    Staff: Mentor

    Althought the correct approach has already been pointed out, the equation above deserves a further comment. You can't get to the equation above from the one you showed in a previous post:
    If you multiply out your factored form, you get only two terms, not the three shown just above.
     
  9. Apr 23, 2009 #8
    Yeah I see what you mean Mark44, Teachers always tell you to double check doing what you just did. Maybe I need to start doing that more.
     
  10. Apr 24, 2009 #9

    Mark44

    Staff: Mentor

    Yeah, maybe you should, especially when you're in the early stages of learning something.
     
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