Answer
$\csc\theta=2$
$\sin\theta=\frac{1}{2}$
$ \cos\theta=-\frac{\sqrt 3}{2}$
$\sec\theta=-\frac{2\sqrt 3}{3}$
$\tan\theta=-\frac{\sqrt 3}{3}$
$\cot\theta=-\sqrt 3$
Work Step by Step
$\csc\theta=2$
$\sin\theta=\frac{1}{\csc\theta}=\frac{1}{2}$
$\cos^{2}\theta=1-\sin^{2}\theta=1-(\frac{1}{2})^{2}=\frac{3}{4}$
$\cos\theta=\pm\sqrt {\frac{3}{4}}$
$\cos\theta$ is negative in the second quadrant.
$\implies \cos\theta=-\frac{\sqrt 3}{2}$
$\sec\theta=\frac{1}{\cos\theta}=-\frac{2}{\sqrt 3}=-\frac{2\sqrt 3}{3}$
$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{1}{2}}{-\frac{\sqrt 3}{2}}=-\frac{1}{\sqrt 3}=-\frac{\sqrt 3}{3}$
$\cot\theta=\frac{1}{\tan\theta}=-\sqrt 3$
