To evaluate
[tex]co\sec (\frac{11\pi}{3})[/tex]But we need to understand the identity of cosecant
[tex]\text{cosecant}\theta=\frac{1}{\text{sin}\theta}[/tex][tex]co\sec (\frac{11\pi}{3})=\frac{1}{\sin(\frac{11\pi}{3})}[/tex]Simplifying further
[tex]\frac{1}{\sin(\frac{11\pi}{3})}=\frac{1}{\sin (660)}=\frac{1}{\frac{-\sqrt[]{3}}{2}}[/tex][tex]\Rightarrow\frac{-2}{\sqrt[]{3}}[/tex]Rationalizing the denominator
[tex]\frac{-2}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{-2\sqrt[]{3}}{3}[/tex]Thus, the answer is:
[tex]\frac{-2\sqrt[]{3}}{3}[/tex]