# Solve for tan(θ)

1. Jul 10, 2016

### Eagertolearnphysics

1. The problem statement, all variables and given/known data
1 ≤ μ (tan(θ)+1)/(tan(θ)-1)

2. Relevant equations

3. The attempt at a solution
1 - (tan(θ)-1)/(tan(θ)+1) ≤ μ

Last edited: Jul 10, 2016
2. Jul 10, 2016

### Ray Vickson

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

3. Jul 10, 2016

### Eagertolearnphysics

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

4. Jul 10, 2016

### Ray Vickson

Are you unable to show us your attempts?

5. Jul 11, 2016

### James R

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

6. Jul 11, 2016

### haruspex

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.

7. Jul 11, 2016

### haruspex

It's in the thread title. The requirement is to turn it into some bounds on tan(θ), as a function of μ presumably.

8. Jul 12, 2016

### James R

9. Jul 12, 2016

### 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?

10. Jul 12, 2016

### Ray Vickson

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