Solve for tan(θ) | Homework Equation

[Eagertolearnphysics]

Homework Statement

1 ≤ μ (tan(θ)+1)/(tan(θ)-1)

Homework Equations

The Attempt at a Solution

1 - (tan(θ)-1)/(tan(θ)+1) ≤ μ[/B]

 

[Ray Vickson]

Homework Statement

1 ≤ μ (tan(θ)+1)/(tan(θ)-1)

Homework Equations

The Attempt at a Solution

PF Rules require you to show your work and your own efforts to solve the problem.

 

[Eagertolearnphysics]

PF Rules require you to show your work and your own efforts to solve the problem.

It's the last step I could get in a bigger problem and I really tried.

 

[Ray Vickson]

It's the last step I could get in a bigger problem and I really tried.

Are you unable to show us your attempts?

 

[James R]

Homework Statement

1 ≤ μ (tan(θ)+1)/(tan(θ)-1)

What are you supposed to show? Are there values for $\mu$ or $\theta$?

 

[haruspex]

1 - (tan(θ)-1)/(tan(θ)+1) ≤ μ

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.
Since this is an inequality, you have to be careful the inequality is still true after each step. This is because if you multiply or divide both sides by something, and that thing turns out to be negative, the inequality will reverse.

 

[haruspex]

What are you supposed to show? Are there values for $\mu$ or $\theta$?

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]

Sorry. I didn't read the thread title!

 

[Irene Kaminkowa]

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?

 

[Ray Vickson]

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?

There are really four cases. If $T \equiv \tan(\theta)$, then we can have
$$\begin{array}{c}<br /> T < -1\\<br /> -1 \leq T < 1 \\<br /> T = 1\\<br /> T > 1 <br /> \end{array}$$
Knowing the sign of $\mu$ will eliminate one or more of these cases.