Answer
tan t = $\frac{\sqrt 2}{4}$
csc t = 3
sec t = $\frac{3\sqrt 2}{4}$
cot t = 2$\sqrt 2$
Work Step by Step
tan t is computed by $\frac{sin t}{cos t}$
tan t = $\frac{sin t}{cos t}$
=$\frac{\frac{1}{3}}{\frac{2\sqrt 2}{3}}$ =$\frac{1}{2\sqrt 2}$*$\frac{\sqrt 2}{\sqrt 2}$ = $\frac{\sqrt 2}{4}$
csc t = $\frac{1}{sin t}$ = $\frac{1}{\frac{1}{3}}$ =3
sec t = $\frac{1}{cos t}$ = $\frac{1}{\frac{2\sqrt 2}{3}}$ = $\frac{3}{2\sqrt 2}$ * $\frac{\sqrt 2}{\sqrt 2}$ = $\frac{3\sqrt 2}{4}$
cot t = $\frac{1}{tan t}$ = $\frac{1}{\frac{1}{2\sqrt 2}}$ = 2$\sqrt 2$
