Answer
$sin~x=-\frac{\sqrt {21}}{5}$
$cos~x=-\frac{2}{5}$
$tan~x=\frac{\sqrt {21}}{2}$
$cot~x=\frac{2\sqrt {21}}{21}$
$csc~x=-\frac{5\sqrt {21}}{21}$
$sec~x=-\frac{5}{2}$
Work Step by Step
$cos~x\lt0$
$tan~x=\frac{sin~x}{cos~x}\gt0$
We can conclude that:
$sin~x\lt0$
$cot~x=\frac{1}{tan~x}\gt0$
$sec~x=\frac{1}{cos~x}\lt0$
$csc~x=\frac{1}{sin~x}\lt0$
$sin^2x+cos^2x=1$
$sin^2x=1-\frac{4}{25}=\frac{21}{25}$
$sin~x=-\frac{\sqrt {21}}{5}$
$tan~x=\frac{sin~x}{cos~x}=\frac{-\frac{\sqrt {21}}{5}}{-\frac{2}{5}}=\frac{\sqrt {21}}{2}$
$cot~x=\frac{x}{y}=\frac{-\frac{2}{5}}{-\frac{\sqrt {21}}{5}}=\frac{2}{\sqrt {21}}=\frac{2\sqrt {21}}{21}$
$csc~x=\frac{1}{sin~x}=\frac{1}{-\frac{\sqrt {21}}{5}}=-\frac{5}{\sqrt {21}}=-\frac{5\sqrt {21}}{21}$
$sec~x=\frac{1}{cos~x}=\frac{1}{-\frac{2}{5}}=-\frac{5}{2}$
