If $$\alpha = 3 \sin^{-1} \left(\frac{6}{11}\right)$$ and $$\beta = 3 \cos^{-1} \left(\frac{4}{9}\right) where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)

A

$$\cos \beta > 0$$

B

$$\sin \beta < 0$$

C

$$\cos (\alpha + \beta) > 0$$

D

$$\cos \alpha < 0$$