(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Expand cos z into a Taylor series about the point z_0 = (pi)/2

With the aid of the identity

cos(z) = -sin(z - pi/2)

2. Relevant equations

Taylor series expansion for sin

sinu = \sum^{infty}_{n=0} (-1)^n * \frac{u^{2n+1}}{(2n+1)!}

and the identity as given above

3. The attempt at a solution

I've subbed in -sin(z- pi/2) into the identity my first prob was how to deal with the negative in front of the sin so I've done

u = z-pi/2

-sin(z-(pi/2)) = -(z-(pi/2)) + 1/3! * (z-(pi/2))^3 - 1/5! * (z-(pi/2))^5

So if that is even correct (because I'm not sure about where to put the negative signs... then what does it mean when it says "about the point" z_0 = (pi/2)

How do I sub that in to my answer???

Any suggestions will be much appreciated

Thanks

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# Homework Help: The Taylor series expansion for sin about z_0 = (pi/2)

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