Re: Cosine Product Limit

In article
<christian.bau-ACF8A4.23345611062005@xxxxxxxxxxxxxxxxxxxxxxxx>,
Christian Bau <christian.bau@xxxxxxxxxxxxxxxxxxxx> wrote:

> > > How do I evaluate the cosine product: cos(x)*cos(2x)*...*cos(nx) using
> > > the Taylor series?
> > >
> > Masochistically, unless you're expecting us to do it you vile sadist. ;-)
>
> You only need it up to x^2 plus a O (x^4).
>
> cos x = 1 - x^2 / 2 + O (x^4)
> cos nx = 1 - n^2 x^2 / 2 + O (x^4) for any fixed n.
>
> Product from cos x to cos nx:
>
> 1 - (sum k^2 for 1 <= k <= n) * x^2 / 2 + O (x^4)
>
> Then the answer is the same.

Right, and a student learns a lot more using that idea I think.
.

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