How do I simplify this inequality

MeMoses · Sep 16, 2012

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

SammyS · Sep 16, 2012

MeMoses said: ↑

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

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).

MeMoses · Sep 16, 2012

Thanks, that's all I needed

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