- #1
laura_a
- 66
- 0
Homework Statement
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)
Homework 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
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 into my answer?
Any suggestions will be much appreciated
Thanks