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