Question: Chebyshev polynomial to write a program

Chebyshev polynomials have the form:


Tn(x) = cos(n*arccos(x))


orthogonality interval is (-1, 1) for n = (2, 3, 4, 5, 6) write polynomials, then draw the charts in the range of orthogonality.

I have no idea how to write a program that can solve this polynomial. It has yet to be: a description of the algorithm and the detailed description of how to solve the problem with comments next steps.

I am dark in this topic and could someone help me, even to a certain extent I would be very grateful.

Thank you in advance for your help. :)

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