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Math Help - What is this the expansion of?

  1. #1
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    What is this the expansion of?

    I'm guessing this is a trigonometric expansion, just not sure which one.

    1-x/2+x^2/24-x^3/720+x^4/40320+....
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  2. #2
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    Notice how the coefficients match those of \cos x?

    \cos ({\color{red}x}) = 1 - \frac{{\color{red}x}^2}{2} + \frac{{\color{red}x}^4}{24}- \frac{{\color{red}x}^6}{720} + \frac{{\color{red}x}^8}{40320} + \cdots

    Now think a little and try to make the necessary adjustments to the powers ...
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  3. #3
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    Is the expansion of cos(x) not

    cos(x)=1-x^2/2+x^4/24-x^6/720+x^8/40320+... ? (sorry didn't realise you'd edited)

    but yeah I was thinking it had something to do with cos, just can't figure it out.

    Also I have another expansion I'm interested in...

    1-x/6+x^2/120-x^3/5040+...

    this has something to do with sin hasn't it?
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  4. #4
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    would it be fair to say my expansion is cos(sqrt(x)) ?
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