Answer
$sin~x=-\frac{4\sqrt {65}}{65}$
$cos~x=-\frac{7\sqrt {65}}{65}$
$tan~x=\frac{4}{7}$
$cot~x=\frac{7}{4}$
$sec~x=-\frac{\sqrt {65}}{7}$
$csc~x=-\frac{\sqrt {65}}{4}$
Work Step by Step
$sin~x\lt0$
$cot~x=\frac{cos~x}{sin~x}\gt0$
We can conclude that:
$cos~x\lt0$
$tan~x=\frac{1}{cot~x}\gt0$
$sec~x=\frac{1}{cos~x}\lt0$
$csc~x=\frac{1}{sin~x}\lt0$
$csc^2x=cot^2x+1=\frac{49}{16}+1=\frac{65}{16}$
$csc~x=-\frac{\sqrt {65}}{4}$
$sin~x=\frac{1}{csc~x}=-\frac{4}{\sqrt {65}}=-\frac{4\sqrt {65}}{65}$
$tan~x=\frac{1}{cot~x}=\frac{4}{7}$
$sec^2x=tan^2x+1=\frac{16}{49}+1=\frac{65}{49}$
$sec~x=-\frac{\sqrt {65}}{7}$
$cos~x=\frac{1}{sec~x}=-\frac{7}{\sqrt {65}}=-\frac{7\sqrt {65}}{65}$
