Chebyshev polynomial of order 11

I've spent hours working on this 8 problem assignment and have only 1 done. I've searched, read the textbook, and looked for video tutorials, but nothing can help me understand what to do. Here is the question:

Calculate the Chebyshev Polynomial of order 11. (I.E. find the polynomial $\displaystyle P_{11}(x)$ such that $\displaystyle cos 11x = P_{11}(cosx)$

This is what I have:

$\displaystyle (1-x^{2})y'' - xy' +n^2 y = 0

$

$\displaystyle t= \pi/2$

$\displaystyle

P_{11}(cost)=cos(11t)$

$\displaystyle P_{11}(0)=0$

$\displaystyle y=P_n(x)$

$\displaystyle cosnx = P_n(cos(x))$

Thanks.