Answer
$$\cos \theta = \frac{5}{{13}},\,\tan \theta = \frac{{12}}{5},\,\,\cot \theta = \frac{5}{{12}},\,\,\sec \theta = \frac{{13}}{5},\,\,\csc \theta = \frac{{13}}{{12}}$$
Work Step by Step
$$\eqalign{
& {\text{We have that }}\theta = {\sin ^{ - 1}}\frac{{12}}{{13}} \cr
& \cr
& \sin \theta = \frac{{12}}{{13}} = \frac{{{\text{opposite side}}}}{{{\text{hypotenuse}}}} \cr
& {\text{Adjacent side}} = \sqrt {{{13}^2} - {{12}^2}} \cr
& {\text{Adjacent side}} = 5 \cr
& \cr
& {\text{Then,}} \cr
& \cos \theta = \frac{5}{{13}} \cr
& \tan \theta = \frac{{12}}{5} \cr
& \cot \theta = \frac{5}{{12}} \cr
& \sec \theta = \frac{{13}}{5} \cr
& \csc \theta = \frac{{13}}{{12}} \cr} $$
