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.
cos2m= 2cos^2 m -1
cos (A+B)= cosAcosB-sinAsinB
Cos(2m+m)=cos3m=(2cos^2m-1)cos(m) - sin(m)(2sin(m)cos(m))
=2cos^3(m) - cos(m) - 2(sin^2m)cos(m)
=2cos^3(m) - cos(m) - 2(1-cos^2(m))cos(m)
=2cos^3(m) - cos(m) -2cos(m) +2cos^2(m)
Plz thank if u like this.