Elipse dos Erros

$$M^2 = 4\sigma_{xy}^2 + (\sigma_x^2 - \sigma_y^2)^2$$

$$\sigma^2 = 0.5(\sigma_x^2 + \sigma_y^2 \pm M)$$

$$\tan(2t) = \frac{2\sigma_{xy}}{\sigma_x^2 - \sigma_y^2}$$

$$\sin(2t) = \frac{2\sigma_{xy}}{M}$$

$$\cos(2t) = \frac{\sigma_x^2 - \sigma_y^2}{M}$$

Tabela de Sinais para

Tabela de Sinais para $\tan(2t)$:

$\sigma_{xy}$	$\sigma_x^2 - \sigma_y^2$	Quadrante 2t
+	+	1
+	-	2
-	-	3
-	+	4