Answer
$sin~x=-\frac{\sqrt 5}{3}$
$cos~x=\frac{2}{3}$
$tan~x=-\frac{\sqrt 5}{2}$
$cot~x=-\frac{2\sqrt 5}{5}$
$csc~x=-\frac{3\sqrt 5}{5}$
$sec~x=\frac{3}{2}$
Work Step by Step
$sin~x\lt0$
$cos~x\gt0$
We can conclude that:
$tan~x=\frac{sin~x}{cos~x}\lt0$
$cot~x=\frac{cosx}{~sin~x}\lt0$
$csc~x=\frac{1}{sin~x}\lt0$
$sec~x=\frac{1}{cos~x}\gt0$
$cos^2x+sin^2x=1$
$sin^2x=1-\frac{4}{9}=\frac{5}{9}$
$sin~x=-\frac{\sqrt 5}{3}$
$tan~x=\frac{sin~x}{cos~x}=\frac{-\frac{\sqrt 5}{3}}{\frac{2}{3}}=-\frac{\sqrt 5}{2}$
$cot~x=\frac{cos~x}{sin~x}=\frac{\frac{2}{3}}{-\frac{\sqrt 5}{3}}=-\frac{2}{\sqrt 5}=-\frac{2\sqrt 5}{5}$
$csc~x=\frac{1}{sin~x}=-\frac{3}{5}=-\frac{3\sqrt 5}{5}$
$sec~x=\frac{1}{cos~x}=\frac{3}{2}$
