α = 3 sin^–1 $\left(\frac{6}{11}\right)$

${\text{sin}}^{–\text{1}}\left(\frac{1}{2}\right)\mathrm{ }<{\text{ sin}}^{–\text{1}}\mathrm{ }\left(\frac{6}{11}\right)<{\text{ sin}}^{–1}\left(\frac{1}{\sqrt{2}}\right)$

$\text{3}\left(\frac{\mathrm{\pi }}{6}\right)<{\text{ 3 sin}}^{–\text{1}}\left(\frac{6}{11}\right)\mathrm{ }<\text{ 3}\left(\frac{\mathrm{\pi }}{4}\right)$

$\frac{\mathrm{\pi }}{2}<\mathrm{\alpha }<\frac{3\mathrm{\pi }}{4}$

$\therefore \mathrm{\alpha }\in$ II^nd quadrant

$\mathrm{\beta }={\text{ 3 cos}}^{–\text{1}}\mathrm{ }\left(\frac{4}{9}\right)$

${\text{cos}}^{–\text{1}}\mathrm{ }\left(\frac{1}{2}\right)<{\text{ cos}}^{–\text{1}}\left(\frac{4}{9}\right)\mathrm{ }<{\text{ cos}}^{–\text{1}}\left(\frac{\sqrt{6}-\sqrt{2}}{8}\right)$

$\text{3 }\left(\frac{\mathrm{\pi }}{3}\right)<\text{b}<\text{ 3}\frac{5\mathrm{\pi }}{12}$

$\mathrm{\pi }<\mathrm{\beta }<\frac{5\mathrm{\pi }}{4}\Rightarrow \mathrm{\beta }\in$ III^rd quadrant