## Behaviour of Infinite Trigonometric Series [closed]

I made a journal on the behaviour of functions such as

Infinite series of

1.sin(sin(sin(........(x)))
2.cos(cos(cos(........(x)))
3.tan(tan(tan(........(x)))
4.cos(sin(sin(........(x))) x cos(cos(sin(....(x))) x cos(cos(cos(....(x))) x ....... Infinite
5.-sin(cos(cos(....(x))) x -sin(-sin(cos(....(x))) x (-sin(-sin(-sin(.....(x))).... Infinite

I found the values of the above functions for all values of "x" both analytically and graphically and also mentioned a way to plot the rough graphical sketches of any of the the trigonometric composite functions.For ex.Using my method we can plot the graphs of

cos(sin(x),cos(cos(x)),sin(cos(x)) or any such composite functions with ease without a calculator or a graph plotter.

Will this be a good contribution ? Can you do this easily or is this challenging..Please give your opinions

I'm a student of 16 Years where do you think my article can be sent to ? I want to know which organisations would take time in reading and publishing my journals.I hope age factor doesn't count.Even if it did,What are the appropriate institutions.

Thanking You,
Sai Krishna Deep

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Dear Sai Krishna Deep: This type of investigation is very valuable for you to learn about the behavior of functions. But I don't think most research journals will be too interested in your results. It's been a while since I've read Math Mag maa.org/pubs/mathmag.html or College Math Journal maa.org/pubs/cmj.html but they are possibilities. You should consult with a local faculty member and get their help and advice before, during, and after the submission process. – Theo Johnson-Freyd Jul 20 2011 at 16:59
All that being said, I worry that your question above is not really about "research mathematics" (narrowly defined), and so probably isn't appropriate here. You may want to check out some of the websites listed in the FAQ mathoverflow.net/faq . – Theo Johnson-Freyd Jul 20 2011 at 17:00
I'm going to vote to close, because this isn't really phrased as a specific research problem. But the question of iteration of functions such as sin and cos is actually quite interesting, and I'm sure that there are plenty of research level questions one could ask about the dynamics of such functions, especially over the complex numbers. So you might want to read an intro to discrete dynamics books to get an idea of the sorts of problems that are studied in this area. – Joe Silverman Jul 20 2011 at 17:11
If you can find a local faculty member who is willing to endorse the paper, you can also begin by putting it on arXiv. Like Joe Silverman said, things related to iterations of functions can be interesting when considered from the dynamical system perspective, but until we are able to see what you've done, we can't tell you whether the result is interesting or important. – Willie Wong Jul 20 2011 at 17:41
For what I think is an interesting question on iterated trig functions, see the MSE question, "Fekete's conjecture on repeated applications of the tangent function": math.stackexchange.com/questions/6791 – Joseph O'Rourke Jul 20 2011 at 18:19