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