# Math Help - What is this the expansion of?

1. ## What is this the expansion of?

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

$1-x/2+x^2/24-x^3/720+x^4/40320+....$

2. 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 ...

3. 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?

4. would it be fair to say my expansion is $cos(sqrt(x))$ ?