Publishing journals in mathematics.

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I want to ask if I am to publish any research paper on trigonometric function. Where is the best place to do that and what field of mathematics can it be categorized?

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If you have found something new concerning trigonometric functions there are a number of online publishers, some free. From your post though one cannot tell what exactly you desire to publish (content is everything). I wouldn't recommend trying to publish anything without first finding either an application or a good reason for the paper. Moreover, publishing trivial matters could actually hurt your resume. ArXiv is a good site to have your paper peer reviewed before going for more formal publishing.

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Have a look at the Mathematics section of arXiv. You can find it at: http://arxiv.org/

Others mentioned that it would "hurt your resume" if you published something "trivial". I believe the only way that can happen is if you publish in a very poor quality journal, and/or pay to have your work published. Don't do that!

A good quality journal will not accept a paper that is trivial, and that is your best chance for good standard.

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Depending on what's in the paper, you might try The College Mathematics Journal.