The discussion revolves around an inequality involving the tangent function, specifically the expression 1 ≤ μ (tan(θ)+1)/(tan(θ)-1). Participants are attempting to analyze the implications of this inequality in the context of the variable μ and the angle θ.
The discussion is ongoing, with participants exploring different interpretations of the inequality and the conditions under which it holds. Some guidance has been offered regarding careful manipulation of the inequality, but no consensus has been reached on the specific values or bounds for tan(θ).
There are mentions of the need for specific values for μ or θ, and participants are considering various cases for tan(θ) based on the sign of μ. The original poster's attempts are noted, but the completeness of their work is questioned.
Eagertolearnphysics said:Homework Statement
1 ≤ μ (tan(θ)+1)/(tan(θ)-1)
Homework Equations
The Attempt at a Solution
It's the last step I could get in a bigger problem and I really tried.Ray Vickson said:PF Rules require you to show your work and your own efforts to solve the problem.
Eagertolearnphysics said:It's the last step I could get in a bigger problem and I really tried.
What are you supposed to show? Are there values for ##\mu## or ##\theta##?Eagertolearnphysics said:Homework Statement
1 ≤ μ (tan(θ)+1)/(tan(θ)-1)
That's wrong. Try that again, but take it in easy steps. A step consists of performing a single operation on one side, and the same operation on the other side. Be clear at each step what operation you are performing on each side.Eagertolearnphysics said:1 - (tan(θ)-1)/(tan(θ)+1) ≤ μ
It's in the thread title. The requirement is to turn it into some bounds on tan(θ), as a function of μ presumably.James R said:What are you supposed to show? Are there values for ##\mu## or ##\theta##?
Irene Kaminkowa said:Consider three options
tan(θ) <1
tan(θ) >1
tan(θ) = 1
And what is μ? Is it positive? Can it be negative or 0?