# Trascendental equation

1. Mar 11, 2009

### mike79

Hi everybody,

can anyone help me in finding the analytic solution of the trascendental equation in the attached file?

A1, alfa1, alfa2, a and b are constants.
is it possible to solve it by means of Mathematica?

thanks
Michele

#### Attached Files:

• ###### equation.doc
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2. Mar 11, 2009

### Santa1

Just write it in tex, I can't view it.

3. Mar 11, 2009

### mike79

A1*(tan(xa/alfa2)/tan(xa/alfa1))-tan(xa/alfa2)*tan(xb/alfa2)-A1*(tan(xb/alfa2)/tan(xa/alfa1))=1

thanks again

4. Mar 11, 2009

### qntty

Here's the equation in tex

$$\frac{A_1 \cdot \tan{ax / \alpha_2}}{\tan{ax / \alpha_1}} - \tan{ax / \alpha_2} \cdot \tan{bx / \alpha_2} - \frac{A_1 \cdot \tan{bx / \alpha_2}}{\tan{\ax / \alpha_1}} = 1$$

Last edited: Mar 12, 2009
5. Mar 12, 2009

### HallsofIvy

Staff Emeritus
That appears to be a single equation in two different variables, xa and xb. It will not have a single solution.

6. Mar 12, 2009

### mike79

x is the only variable. a and b are real constants. you have to read x*a and x*b and not xa and xb

7. Mar 12, 2009

### csprof2000

So what you really have is

A*tan(a'x)/tan(b'x) - tan(a'x)*tan(c'x) - A*tan(c'x)/tan(b'x) = 1

For appropriate choices of a', b', and c'.

8. Mar 12, 2009

Exactly