Answer
$\sin{\theta} =-0.41$
$\cos{\theta} =-0.91 $
$\tan{\theta} =0.45$
$\csc{\theta} = -2.45$
$\sec{\theta} =-1.09$
$\cot{\theta} =2.22 $
Work Step by Step
$\csc{\theta} = -2.45$
$\sin{\theta} = \dfrac{1}{\csc{\theta}} = \dfrac{1}{-2.45} \approx -0.41$
$\because \theta \in QIII \hspace{20pt} \therefore \cos{\theta}$ is negative.
$\cos{\theta} = -\sqrt{1-\sin^2{\theta}} = - \sqrt{1-(-0.41)^2} \approx -0.91 $
$\tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}} = \dfrac{-0.41}{-0.91} \approx 0.45$
$\sec{\theta} = \dfrac{1}{\cos{\theta}} = \dfrac{1}{-2.45} \approx -1.09$
$\cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}} = \dfrac{-0.91}{-0.41} \approx 2.22 $
