1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

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

    [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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: How do I simplify this inequality
  1. How do i do this? (Replies: 1)

  2. How do i do this? (Replies: 5)