# Tablas trigonométricas

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

$$R cos(x + \theta) = A cos(x) - B sen(x)$$

donde

$$R = \sqrt{A^2+B^2}$$ $$\theta = tan^{-1}(\frac{B}{A})$$ $$A = R cos(\theta)$$ $$B = R sen(\theta)$$