The irrationality measure of π as seen through the eyes of cos(n)

For different values of \γ \≥ 0, analysis of the end behavior of the aₙ = cos (n)n^\γ yields a strong connection to the measure of \π. We show that if \ |cos n|n² \≠1, then the irrationality measure of \π is exactly 2. We also give some evidence to support the conjecture that \μ(\π)=2, based on the of some startling subsequences of cos(n)ⁿ.