Recall the following identities:
[tex]\begin{gathered} \tan (t)=\frac{\sin (t)}{\cos (t)} \\ \csc (t)=\frac{1}{\sin (t)} \\ \sec (t)=\frac{1}{\cos (t)} \\ \cot (t)=\frac{\cos (t)}{\sin (t)} \end{gathered}[/tex]
Since sin(t)=12/13 and cos(t)=5/13, then:
[tex]\begin{gathered} \tan (t)=\frac{(\frac{12}{13})}{(\frac{5}{13})} \\ =\frac{12}{5} \end{gathered}[/tex][tex]\begin{gathered} \csc (t)=\frac{1}{(\frac{12}{13})} \\ =\frac{13}{12} \end{gathered}[/tex][tex]\begin{gathered} \sec (t)=\frac{1}{(\frac{5}{13})} \\ =\frac{13}{5} \end{gathered}[/tex][tex]\begin{gathered} \cot (t)=\frac{(\frac{5}{13})}{(\frac{12}{13})} \\ =\frac{5}{12} \end{gathered}[/tex]
