My Math Forum Solve for x when a trig function equals a polynomial?

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 January 11th, 2014, 12:53 PM #1 Banned Camp   Joined: Dec 2013 Posts: 34 Thanks: 1 Solve for x when a trig function equals a polynomial? I recently came across an interesting type of equation I had completely forgotten about--the kind where a trig function is equal to a polynomial (example below): sin(x) = -(x^2 + 6x - 10)/210 Now, literally, this says sin(x) equals the polynomial on the right at specific points. The only explanations I've gotten on how to solve problems like these are to use a graphing calculator or "Newton's Method" to approximate intersections. Neither of these methods have ever yielded satisfying solutions, though (also, I don't really 'get' Newton's Method well, and it's still only an approximation). How do we find EXACT solutions to these kinds of equations? I am seeking insight; mathaholics, get in here!
 January 11th, 2014, 01:02 PM #2 Senior Member     Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics Re: Solve for x when a trig function equals a polynomial? As far as I know, there is not a method to solve this kind of equations analytically. The only exception is when the polynomial is a constant. So I afraid, you'll have to use some kind of numerical methods to solve those equations.

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# -cos x equal to trignometric

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