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Question: Finding pi with nth taylor poly arctan(x)

Question:Finding pi with nth taylor poly arctan(x)

bluestuff 12 Maple
November 08 2009
0
alright being ragging for a couple hours now and have finally come to this place for help so here goes. The math question is the following "Have Maple compute the Nth Taylor polynomial for arctan(x) about x = 0. So now you have a formula that looks like: π≈ 4 times the Nth Taylor polynomial for arctan, evaluated at x = 1. There's nothing trigonometric on the right-hand side of this formula. It's just a polynomial. So we can use this to approximate π numerically. Use it to find π to 5 decimal places. " I have created a taylor poly function arctan(x) about x=0 with Tpoly := N arrow; convert(taylor(arctan(x), x = 0, N+1), polynom) used digits=:5 to display 5 digits however i am confused on how to use the Nth taylor poly to find pi to 5 digits. I thought at first to input large Tpoly functions such as Tpoly(1000) but the accuracy of these digits is fairly terrible in comparison to pi and I know I'm missing something stupidly obvious. Thx in advance.
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