sin(x) = sin(alpha): x = npi + (-1)^n * alpha. cos(x) = cos(alpha): x = 2npi +/- alpha. tan(x) = tan(alpha): x = n*pi + alpha. Key insight: the (-1)^n in the sine formula alternates between adding and subtracting alpha at each multiple of pi. Always express the RHS using a standard angle before applying these formulas.