Re: Multiple angle help!!

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Article #96

#96

From: Michael Hardy
Date: Sun, 08 Sep 1996 00:00

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	In article <01bb9bf3$49e01100$1b5c0fcb@default>,
		Al <joiced@omen.com.au> wrote:


>cos 4x = 8cos^4 x - 8cos^2 x + 1)
>
>As the values of n increase, so too does the level of complexity of its
>expansion.
>
>I' ve established certain patterns and rules for the expansion in terms of 
>sin nx or cos nx. But am at a loss to find a diffinitive link (or rule)
>between the two. 


	Go to the library and look up "Chebyshev ploynomials".  Cos(nx) can
be written as an n-th degree polynomial in cos(x).  cos(nx)=P(cos(x)).  The
polynomial P is the n-th "Chebyshev polynomial".  You might find useful
stuff in books on "orthogonal polynomials".


	Mike Hardy

Michael Hardy
hardy@stat.umn.edu

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From: hardy@umnstat.stat.umn.edu (Michael Hardy)
Subject: Re: Multiple angle help!!
Date: 1996/09/08
Message-ID: <50v4p1$n21@epx.cis.umn.edu>
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organization: School of Statistics, University of Minnesota
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