Answer
$sin~x=\frac{2\sqrt {13}}{13}$
$cos~x=\frac{3\sqrt {13}}{13}$
$tan~x=\frac{2}{3}$
$cot~x=\frac{3}{2}$
$sec~x=\frac{\sqrt {13}}{3}$
$csc~x=\frac{\sqrt {13}}{2}$
Work Step by Step
$cos~x\gt0$
$tan~x=\frac{sin~x}{cos~x}\gt0$
We can conclude that:
$sin~x\gt0$
$cot~x=\frac{1}{tan~x}\gt0$
$sec~x=\frac{1}{cos~x}\gt0$
$csc~x=\frac{1}{sin~x}\gt0$
$sec^2x=tan^2x+1=\frac{4}{9}+1=\frac{13}{9}$
$sec~x=\frac{\sqrt {13}}{3}$
$cos~x=\frac{1}{sec~x}=\frac{3}{\sqrt {13}}=\frac{3\sqrt {13}}{13}$
$cot~x=\frac{1}{tan~x}=\frac{3}{2}$
$csc^2x=cot^2x+1=\frac{9}{4}+1=\frac{13}{4}$
$csc~x=\frac{\sqrt {13}}{2}$
$sin~x=\frac{1}{csc~x}=\frac{2}{\sqrt {13}}=\frac{2\sqrt {13}}{13}$
