Answer
$sinx=-\frac{2\sqrt 2}{3}$
$tan x=2\sqrt 2$
$cscx=-\frac{3}{2\sqrt 2}=-\frac{3\sqrt 2}{4}$
$sec x=-3$
$cot x=\frac{1}{2\sqrt 2}=\frac{\sqrt 2}{4}$
Work Step by Step
Since $cosx=-\frac{1}{3}$, we can label the adjacent side as having length 1 and the hypotenuse as having length 3.
Then Pythagorean Theorem gives
opposite side $=\sqrt {3^{2}-1^{2}}=2\sqrt 2$
The other five trigonometric functions are given as follows:
$sinx=-\frac{2\sqrt 2}{3}$
$tan x=2\sqrt 2$
$cscx=-\frac{3}{2\sqrt 2}=-\frac{3\sqrt 2}{4}$
$sec x=-3$
$cot x=\frac{1}{2\sqrt 2}=\frac{\sqrt 2}{4}$
