Answer
$\tan{\theta}=-\dfrac{3}{4}$
$\csc{\theta} =- \dfrac{5}{3}$
$\sec{\theta} =\dfrac{5}{4}$
$\cot{\theta} =-\dfrac{4}{3}$
Work Step by Step
$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$
$\therefore \tan{\theta}= \dfrac{-\dfrac{3}{5}}{\dfrac{4}{5}}=-\dfrac{3}{4}$
$\csc{\theta} = \dfrac{1}{\sin{\theta}}$
$\therefore \csc{\theta} = \dfrac{1}{-\dfrac{3}{5}}=- \dfrac{5}{3}$
$\sec{\theta} = \dfrac{1}{\cos{\theta}}$
$\therefore \sec{\theta} = \dfrac{1}{\dfrac{4}{5}}= \dfrac{5}{4}$
$\cot{\theta} = \dfrac{1}{\tan{\theta}}$
$\therefore \cot{\theta} = \dfrac{1}{-\dfrac{3}{4}}= -\dfrac{4}{3}$
