Answer
$sin~x=-\frac{6}{7}$
$cos~x=-\frac{\sqrt {13}}{7}$
$tan~x=\frac{6\sqrt {13}}{13}$
$cot~x=\frac{\sqrt {13}}{6}$
$sec~x=-\frac{7\sqrt {13}}{13}$
Work Step by Step
$csc~x=\frac{1}{sin~x}\lt0$
$tan~x=\frac{sin~x}{cos~x}\gt0$
We can conclude that:
$sin~x\lt0$
$cos~x\lt0$
$cot~x=\frac{1}{tan~x}\gt0$
$sec~x=\frac{1}{cos~x}\lt0$
$sin~x=\frac{1}{csc~x}=\frac{1}{-\frac{7}{6}}=-\frac{6}{7}$
$cos^2x+sin^2x=1$
$cos^2x=1-\frac{36}{49}=\frac{13}{49}$
$cos~x=-\frac{\sqrt {13}}{7}$
$tan~x=\frac{sin~x}{cos~x}=\frac{-\frac{6}{7}}{-\frac{\sqrt {13}}{7}}=\frac{6}{\sqrt {13}}=\frac{6\sqrt {13}}{13}$
$cot~x=\frac{cos~x}{sin~x}=\frac{-\frac{\sqrt {13}}{7}}{-\frac{6}{7}}=\frac{\sqrt {13}}{6}$
$sec~x=\frac{1}{cos~x}=-\frac{7}{\sqrt {13}}=-\frac{7\sqrt {13}}{13}$
