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Expansion of cos 15 x interms of cos

  1. Jan 5, 2012 #1
    I have expanded cos 15x interms of cos. I hope some one who needs it can use it. I have verified this formulae using symbolic matlab: so its geniune

    cos 15*theta = 16384*cos(theta)^15 - 61440*cos(theta)^13 + 92160*cos(theta)^11 - 70400*cos(theta)^9 + 28800*cos(theta)^7 - 6048*cos(theta)^5 + 560*cos(theta)^3 - 15*cos(theta)
     
  2. jcsd
  3. Jan 5, 2012 #2

    Mentallic

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    Thanks, I've been looking everywhere for this!
     
  4. Jan 5, 2012 #3
    One might notice a similarity with the Chebyshev polynomial of 15th degree:

    T15(x)=16384x15-61440x13+92160x11-70400x9+28800x7-6048x5+560x3-15x
     
  5. Jan 6, 2012 #4
    This means that chebyshev function is nothing but a cos function
     
  6. Jan 6, 2012 #5

    AlephZero

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    That's not quite accurate, but [itex]T_n(\cos \theta) = \cos(n \theta)[/itex].
     
  7. Jan 6, 2012 #6

    D H

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    Does [itex]16384 x^{15}-61440 x^{13}+92160 x^{11}-70400 x^9+28800 x^7-6048 x^5+560 x^3-15 x[/itex] look like "a cos function"? It's a polynomial. Like the other Chebychev polynomials, it is a rather useful polynomial.
     
  8. Jan 7, 2012 #7
    I retract my previous statement
     
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