Question

The taylor series for f(X)=sin(X) at a=pie/3 is

sigma (cn(x-pie/3)^(n)). find c0,c1,c2,c3,c4

Answer 1

what is the second statement??

Answer 2

oh just find each C for n=0,1,2,3,4

Answer 3

lol "pie"

Answer 4

\(sin(x) = sin(a) + cos(a) x - sin(a) x^2/2 - cos(a)/x^3/3! + sin(a) x^4/4 + ...\)
\(sin(x) = sin(\pi/3) + cos(\pi/3) x - sin(\pi/3) x^2/2 - cos(\pi/3)/x^3/3! + sin(\pi/3) x^4/4! + ...\)

From above, it can be found by comparing

Answer 5

\( c0 = \sqrt{3}/2\),
\(c1 = 1/2\),
..
..

Answer 6

\[\frac{\sqrt{3}}{2}+\frac{1}{2}
\left(x-\frac{\pi
}{3}\right)-\frac{1}{4}
\sqrt{3} \left(x-\frac{\pi
}{3}\right)^2-\frac{1}{12}
\left(x-\frac{\pi
}{3}\right)^3+\frac{\left(x
-\frac{\pi
}{3}\right)^4}{16
\sqrt{3}}+\frac{1}{240}
\left(x-\frac{\pi
}{3}\right)^5+O\left(\left(
x-\frac{\pi
}{3}\right)^6\right)
\]

Answer 7

wow?? how did you do that??

Answer 8

So, i must have been (x-pi/3) instead of x

how will you get the coefficients of x's ... isn't it going to infinity??