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January 11th, 2014, 12:53 PM   #1
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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!
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January 11th, 2014, 01:02 PM   #2
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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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