# Quick! Where's the Chebyshev Table?

Geometry Level 5

$\large{\begin{eqnarray} \cos(2x) &=& 2\cos^2(x) - 1 \\ \cos(3x) &=& 4\cos^3(x) - 3\cos(x) \\ \cos(4x) &=& 8\cos^4(x) - 8\cos^2(x)+1 \\ \end{eqnarray} }$

Above shows the first 3 examples of writing $$\cos(nx)$$ in terms of a polynomial of $$\cos(x)$$ for positive integer $$n$$.

If we write $$\cos(2015x)$$ in terms of a polynomial of $$\cos(x)$$, what is the coefficient of $$\cos^3(x)$$?

If the value is $$Y$$, submit your answer as $$Y \div 2015$$.

×