Trigonometric Ecuation

[giorgio]

Any suggest about how to solve this ecuation will be appretiated

 

[math] x(\csc(x)+1)=\pi[/math]

 

 

Thanks in advance.

[Fuzzwood]

You can rewrite this to:

 

[math] x/sin(x) + x = pi [/math]

 

What would be a nice value of x so that x is divided by a nice number?

 

PS. Why does my latex fail?

Edited August 26, 2011 by Fuzzwood

[giorgio]

You can rewrite this to:

 

[math] x/sin(x) + x = pi [/math]

 

What would be a nice value of x so that x is divided by a nice number?

 

PS. Why does my latex fail?

 

I understant that trial values for x would give me " pi/2 " ,but I'm trying to find out another method.

 

Thank for the answer.

[ajb]

This seems hard to solve algebraically, if it can be solved in a closed form at all.

 

The easiest thing you could do is plot the function. You will see that there is two solutions.

[imatfaal]

You can rewrite this to:

 

[math] x/sin(x) + x = pi [/math]

 

What would be a nice value of x so that x is divided by a nice number?

 

PS. Why does my latex fail?

 

[math] x/sin(x) + x = pi [/math]

 

[math] \frac{x}{sin(x)} + x = \pi [/math]

 

You need a frd slash \ in front of pi to make it into the greek script and \frac with the top and bottom enclosed in {}

 

PS

by the way the board seems to strip out forward slashes when you inspect others latex

Edited August 30, 2011 by imatfaal

[Schrödinger's hat]

Expanding it in series form doesn't seem to help -- at least with anything I know, other than a numerical approach I don't have a clue.

Wolfram alpha confirms that it's rather ugly.

http://www.wolframalpha.com/input/?i=solve%28x*%28csc%28x%29+%2B+1%29+%3D+pi%29+for+x