Answer
$\Rightarrow \sin x=-\dfrac {4}{5}$
$\tan x=-\dfrac {4}{3}$
$\cot \left( -x\right) =\dfrac {3}{4}$
Work Step by Step
In quadrant 4 only cosine function is positive $sine$ $tan$ and $\cot$ are negative
$\Rightarrow \sin x=-\sqrt {1-\cos ^{2}\theta }=-\sqrt {1-(\dfrac {3}{5})^{2}}=-\dfrac {4}{5}$
$\tan x=\dfrac {\sin x}{\cos x}=\dfrac {-\dfrac {4}{5}}{\dfrac {3}{5}}=-\dfrac {4}{3}$
$\cot \left( -x\right) =-\cot \left( x\right) =-\dfrac {1}{\tan x}=-\dfrac {1}{-\dfrac {4}{3}}=\dfrac {3}{4}$
