How to solve where a maclaurin series intersects a graph

[xaphenx]

I have just finished a unit on constructing taylor and maclaurin polynomials and series.
However I am really lost on how to find the answer to this problem that i found online for the test review and its going to be on my test, I know how to construct a maclaurin polynomial and have a vague sense of how to use it, but since the polynomial is centered at zero and the two graphs don't intersect at zero, isn't there some degree of error?

gahh, I don't understand and would really appreaciate a nudge in the right direction..
Here is the problem:
http://img534.imageshack.us/img534/7917/problemthree.png

 

[csopi]

Because the series is infinite, you cannot treat it as a polynomial equation. However, the left side is just cos (2x), so you need to solve

cos(2x)=2x^3.

This cannot be solved (as far as I know) analytically, the approx. solution is 0.58236.

 

[xaphenx]

thanks much, that makes sense to me now.. Without converting it into cos(2x) though, is that a solvable problem? Like what if you couldn't put that into any abbreviated equation, like sin or cos or e^x or a geometric series?

is it actually possible to solve where a random maclaurin and a graph intersect.. ?