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Trig homework problem

  1. Oct 29, 2006 #1
    How do I show that

    [tex]T_n(x)=\cos(n\arccos(x))[/tex]

    are actually polynomials of degree n?

    If n=2 then

    [tex]T_2(x)=x^2-(1-x^2)[/tex]

    but this seems to break down as n increases.
     
  2. jcsd
  3. Oct 29, 2006 #2

    StatusX

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    So if x=cos(y), you want to show cos(ny) is a nth degree polynomial in cos(y). Induction is usually the first thing to try whenever there's an n knocking about.
     
  4. Oct 29, 2006 #3

    Office_Shredder

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    It also definitely fails for n=1, but since you started with 2, maybe we're ignoring that
     
  5. Oct 29, 2006 #4
    How does it fail for n=1? The function f(x)=x is a polynomial.
     
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