Answer
$sin~x=-\frac{3}{4}$
$cos~x=\frac{\sqrt {7}}{4}$
$tan~x=-\frac{3\sqrt {7}}{7}$
$cot~x=-\frac{\sqrt {7}}{3}$
$csc~x=-\frac{4}{3}$
$sec~x=\frac{4\sqrt {7}}{7}$
Work Step by Step
$sin~x\lt0$
$cos~x\gt0$
We can conclude that:
$tan~x=\frac{sin~x}{cos~x}\lt0$
$cot~x=\frac{cosx}{~sin~x}\lt0$
$csc~x=\frac{1}{sin~x}\lt0$
$sec~x=\frac{1}{cos~x}\gt0$
$cos^2x+sin^2x=1$
$cos^2x=1-\frac{9}{16}=\frac{7}{16}$
$cos~x=\frac{\sqrt {7}}{4}$
$tan~x=\frac{sin~x}{cos~x}=\frac{-\frac{3}{4}}{\frac{\sqrt {7}}{4}}=-\frac{3}{\sqrt {7}}=-\frac{3\sqrt {7}}{7}$
$cot~x=\frac{cos~x}{sin~x}=\frac{\frac{\sqrt {7}}{4}}{-\frac{3}{4}}=-\frac{\sqrt {7}}{3}$
$csc~x=\frac{1}{sin~x}=-\frac{4}{3}$
$sec~x=\frac{1}{cos~x}=\frac{4}{\sqrt {7}}=\frac{4\sqrt {7}}{7}$
