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How do I simplify this inequality

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    So i'm following along with my physics book and I get to the point where
    Mg * abs(sin(θ) - cos(θ)) <= μMg * (cos(θ) + sin(θ)
    Next they say: If tan(θ) >= 1 then
    sin(θ) - cos(θ) <= μ(cos(θ) + sin(θ)) => tan(θ) <= (1+μ) / (1-μ)


    2. Relevant equations



    3. The attempt at a solution
    How do I go from sin(θ) - cos(θ) <= μ(cos(θ) + sin(θ)) to tan(θ) <= (1+μ) / (1-μ)?
    Could someone walk me through this or at least get me started? Thanks
     
  2. jcsd
  3. Sep 16, 2012 #2

    SammyS

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    You get to do most of the walking. (Hopefully, you know by now that that's how we do things here at PF.)

    Take
    [itex]\sin(\theta) - \cos(\theta) \le \mu(\cos(\theta) + \sin(\theta))[/itex]​
    and divide both sides by cos(θ) .

    Simplify, and the only trig function remaining is tan .

    Now, try to isolate tan(θ).
     
  4. Sep 16, 2012 #3
    Thanks, that's all I needed
     
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