Referencia: Leon W Couch Apéndice p653
cos(x \pm y)= cos(x)cos(y) \mp sen(x)sen(y) sen(x \pm y) = sen(x)cos(y) \pm cos(x) sen(y) cos\left( x \pm \frac{\pi}{2}\right) = \mp sen(x) sen\left( x \pm \frac{\pi}{2}\right) = \pm cos(x) cos(2x)= cos^2 (x)- sen^2(x) sen(2x)= 2sen(x)cos(x) 2 cos(x)cos(y) = cos(x-y) + cos(x+y) 2 sen(x)sen(y) = cos(x-y) - cos(x+y) 2 sen(x)cos(y) = sen(x-y) + sen(x+y) 2 cos^2(x) = 1 + cos(2x) 2 sen^2(x) = 1 - cos(2x) 4 cos^3(x) = 3cos(x) + cos(3x) 4 sen^3(x) = 3sen(x) + sen(3x) 8 cos^4(x) = 3 + 4cos(2x) + cos(4x) 8 sen^4(x) = 3 - 4cos(2x) + cos(4x)con magnitud R y fase Θ
donde
R = \sqrt{A^2+B^2} \theta = tan^{-1}(\frac{B}{A}) A = R cos(\theta) B = R sen(\theta)