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