• Support PF! Buy your school textbooks, materials and every day products Here!

How do I simplify this inequality

  • Thread starter MeMoses
  • Start date
  • #1
129
0

Homework Statement


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)


Homework Equations





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
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,238
963

Homework Statement


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)

Homework Equations



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).
 
  • #3
129
0
Thanks, that's all I needed
 

Related Threads for: How do I simplify this inequality

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
4K
Replies
1
Views
1K
Replies
10
Views
2K
Replies
6
Views
722
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
13
Views
1K
Replies
1
Views
2K
Top