Answer
$$2$$
Work Step by Step
$$\eqalign{
& \csc \frac{\pi }{6} \cr
& {\text{convert }}\frac{\pi }{6}{\text{radians to degrees}} \cr
& \frac{\pi }{6}{\text{radians}} = \frac{\pi }{6}\left( {\frac{{{{180}^ \circ }}}{\pi }} \right) \cr
& \frac{\pi }{6}{\text{radians}} = {30^ \circ } \cr
& \csc \frac{\pi }{6} = \csc {30^ \circ } \cr
& {\text{using the }}{30^ \circ }{\text{ - 6}}{{\text{0}}^ \circ }{\text{ - 9}}{{\text{0}}^ \circ }{\text{ triangle to obtain}} \cr
& \csc {30^ \circ } = \frac{{{\text{hyppotenuse}}}}{{{\text{opposite side to the 3}}{{\text{0}}^ \circ }}} \cr
& \csc {30^ \circ } = \frac{2}{1} \cr
& {\text{then }} \cr
& \csc \frac{\pi }{6} = 2 \cr} $$
