Finding Non-Zero Terms and Interval of Convergence for Cycloid Power Series

[mathwiz1234]

Homework Statement

Find the first non-zero terms, the general term for the cycloid power series, and the interval of convergence for the cycloid power series.

cycloid:
y=-a+acos(theta)
x=a(theta)-asin(theta)

Homework Equations

I know that f(a)+ f'(a)(x-a)+ f''(a)(x-a)^2... will give me the right
answer but I don't know how to do this in parametric mode or what
really do other than what I've listed below. Thanks!

The Attempt at a Solution

I know that the basics for taylor polynomials. for a cycloid,


y=-a+acos(theta)
x=a(theta)-asin(theta)

so, dy/dx=-sin(theta)/1-cos(theta)

I also know that d(dy/dx)/dx=d^2y/dx^2

 

[lippyka]

=-cos(theta)/(1-cos(theta))^2But I don't know what to do after that or how to find the first non-zero term, the general term for the cycloid power series, and the interval of convergence for the cycloid power series.