Answer
tan t = $\frac{2\sqrt 5}{5}$
csc t =$\frac{3}{2}$
sec t =$\frac{3\sqrt 5}{5}$
cot t = $\frac{\sqrt 5}{2}$
Work Step by Step
tan t is computed by $\frac{sin t}{cos t}$
tan t = $\frac{sin t}{cos t}$
=$\frac{\frac{2}{3}}{\frac{\sqrt 5}{3}}$ =$\frac{2}{\sqrt 5}$*$\frac{\sqrt 5}{\sqrt 5}$ = $\frac{2\sqrt 5}{5}$
csc t = $\frac{1}{sin t}$ = $\frac{1}{\frac{2}{3}}$ =$\frac{3}{2}$
sec t = $\frac{1}{cos t}$ = $\frac{1}{\frac{\sqrt 5}{3}}$ = $\frac{3}{\sqrt 5}$ * $\frac{\sqrt 5}{\sqrt 5}$ = $\frac{3\sqrt 5}{5}$
cot t = $\frac{1}{tan t}$ = $\frac{1}{\frac{2}{\sqrt 5}}$ = $\frac{\sqrt 5}{2}$
