Please help. I'm taking an honors geometry class and my teacher gave us this problem as extra credit. I unfortunately am having a problem understanding exactly where to go with this one. I understand combination of positive integers but when the cos is thrown in I am confused.
Express cos(3m) as a combination of positive integer powers of cos(m). Use this expression to obtain a cubic polynomial p(x) with rational number coefficients such that x = cos(m) is a root. Graph the resulting polynomial for m = 20 degrees that displays all three of the roots.