Any suggest about how to solve this ecuation will be appretiated

 

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

 

 

Thanks in advance.

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, 201114 yr by 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?

 

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.

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.

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, 201114 yr by imatfaal

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