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) $\cos \alpha<0$
