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Homework Help: Inequalities (trig) + Attempted

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data

    tanx + 3cotx = 4

    2. Relevant equations



    3. The attempt at a solution

    Heres my attempt:

    tanx + 3/tanx - 4 = 0
    (tan^2x -4tanx + 3) / tanx = 0

    tan^2x - 4 tanx + 3

    (tanx - 3 ) (tanx - 1 ) = 0

    tan = 3, tan = 1

    im not sure about tan = 3, but for tan = 1 , pi/4 +180n,
    is this correct? if it is how would i go about findin solutions for tan=3.

    please help,
    thanks.
     
  2. jcsd
  3. Sep 27, 2010 #2

    rock.freak667

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    The same way you solved tanx=1

    tanx=3, the principle angle is tan-1(3)
     
  4. Sep 27, 2010 #3
    how would we represent tan^-1(3) interms of radians ?
    calculators are not allowed in our school, is there a way ?
     
  5. Sep 27, 2010 #4

    rock.freak667

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    Unfortunately there is not.
     
  6. Sep 28, 2010 #5
    hmm..
    so we just find solutions for tan = 1 ?
     
  7. Sep 28, 2010 #6

    eumyang

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    "pi/4 +180n" -> Don't mix degree and radian measure. Also, state what "n" is. You should write
    [tex]\frac{\pi}{4} + n \pi, n \in \mathbb{Z}[/tex]

    No, you still need both solutions. The other could be written as
    [tex]\tan^{-1} 3 + n \pi, n \in \mathbb{Z}[/tex]
     
  8. Oct 2, 2010 #7
    tan^-1(3) + npi
    how do you write that interms of pi?

    i've never seen anything like that. could you please give me an example?
     
  9. Oct 2, 2010 #8

    rock.freak667

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    you can't write tan-1(3) in terms of pi. That is why you have to leave it as is.
     
  10. Oct 2, 2010 #9
    ok, just to make sure.. are my previous steps correct?
    just to double check. thanks
     
  11. Oct 2, 2010 #10

    rock.freak667

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    Yes they are correct.
     
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