Question

I call upon thee greatest physicists to help me solve "n" from this equation:
5.41*arctan(((0.03/n)+n*sin(8.87*n))/(294.4*n*(n^2-1)+(n^2+1)*cos(8.87*n)))-2=0

Written it looks like this:
http://i.imgur.com/Vu1eHEW.png

I'd be very thankful if anyone here would solve this for me. I've been struggling with it for the past few days.

Answer 1

Very unlikely you could solve for n with any ease, with it being embedded in cosines within arctangents, and also polynomials thrown in there.
http://www.wolframalpha.com/input/?i=5.41*arctan(((0.03%2Fn)%2Bn*sin(8.87*n))%2F(294.4*n*(n%5E2-1)%2B(n%5E2%2B1)*cos(8.87*n)))-2%3D0

Answer 2

What did it come from?

Answer 3

At the risk of reading picky, this seems to be a maths question ? Where's the physics relevance ?
Bon voyage
http://perendis.webs.com

Answer 4

So what's the answer of "n" , @agent0smith . I need a solution for n so I could calculate other parameters. It can be approximate, you can use any program you want.

Answer 5

Didn't you see? Even wolframalpha couldn't solve for n. I even tried using a pro account.

Answer 6

Oh I think WA did find n=-1 as a solution.

Answer 7

n= -1 ? @agent0smith

With MATHlab script I got -0.99484037747089273064299820465342

can we declare this as an answer?

Answer 8

Sure. WA showed it on a graph, so it may not have been exactly -1 but close enough

Answer 9

That red dot is the answer?

Answer 10

Can refractive index be negative I wonder?

Answer 11

I actually have a new equation
5.41*arctan(((0.06/n)+2*n*sin(8.87*n))/(0.267*n-(0.267/n)+(n^2+1)*cos(8.87*n)))-2=0

Written it looks like this:

http://i.imgur.com/tW7Dn95.png


I get an answer n=-234.28891252558161414819175592836

Is it normal to get such a refreactive index? Or do you get a different answer?

Answer 12

it would really be better if you just posted the original question. Nobody knows what any of this is about exept you and you keep making the xy problem:

http://meta.stackexchange.com/questions/66377/what-is-the-xy-problem

Mathematica can't solve the equation. At best it can expand it. I tried yesterday, no go.

Answer 13

There's no original question. I just need to solve for n from that equation. ..... ???

Answer 14

wth, the actual question is: "solve for n the following equation:"

$$5.41\tan^{-1}\left[ \frac{\frac{0.03}{n}+n\sin(8.87n)}{(294.4n(n^2-1)+(n^2+1)cos(8.87*n)}\right]-2=0$$

you didn't reach that equation from somewhere else? Because doing:

Solve[-2+5.41 ArcTan[(0.03/n+n Sin[8.87 n])/(294.4 n (-1+n^2)+(1+n^2) Cos[8.87 n])]==0&& n \ [Element] Reals, {n}]

in mathematica gets stuck in an endless loop without results.

I'll give it a go, since human > a program in this stuff but it just seem as tiresome bs of a task then.

Answer 15

Just post the original question. A screenshot of what you were given, because no.