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Taylor Polynomial

  1. Nov 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine the Taylor Series for f(x)=sinx about the center point c=pi/6


    2. Relevant equations
    pn(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...


    3. The attempt at a solution

    f(pi/6) = 1/2
    f'(pi/6) = [tex]\sqrt{3}[/tex]/2
    f''(pi/6) = -1/2
    f'''(pi/6) = -[tex]\sqrt{3}[/tex]/2
    f(4)(pi/6) = 1/2 and the coefficients repeats from here


    What I am stuck on is.. how do I make it so that (-1) will only appear on the 3rd and 4th term... and how do I make it so that [tex]\sqrt{3}[/tex] will only appear on the odd terms?
     
  2. jcsd
  3. Nov 20, 2007 #2

    Office_Shredder

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    If w=x-pi/6 then sinx=sin(w+pi/6)=sin(w)cos(pi/6)+sin(pi/6)cos(w). Try expanding this and see what you get
     
  4. Nov 20, 2007 #3
    I am not sure how that relates to Taylor's Series?
     
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