Answer
$$\tan {30^ \circ } = \frac{{\sqrt 3 }}{3},\,\,\,\,\cot {30^ \circ } = \sqrt 3 ,\,\,\,\,\,\csc {30^ \circ } = 2$$
Work Step by Step
$$\eqalign{
& {\text{from the table we have the following information}} \cr
& \sin {30^ \circ } = \frac{1}{2}{\text{, }}\cos {30^ \circ } = \frac{{\sqrt 3 }}{2}{\text{ and }}\sec {30^ \circ } = \frac{{2\sqrt 3 }}{3} \cr
& {\text{then}}{\text{, using the elementary trigonometric identities we obtain}} \cr
& \tan {30^ \circ } = \frac{{\sin {{30}^ \circ }}}{{\cos {{30}^ \circ }}} = \frac{{1/2}}{{\sqrt 3 /2}} = \frac{1}{{\sqrt 3 }} = \frac{{\sqrt 3 }}{3} \cr
& \cot {30^ \circ } = \frac{1}{{\tan {{30}^ \circ }}} = \frac{1}{{\sqrt 3 /3}} = \sqrt 3 \cr
& \csc {30^ \circ } = \frac{1}{{\sin {{30}^ \circ }}} = \frac{1}{{1/2}} = 2 \cr} $$
