Answer
$\tan{\theta}=\sqrt{3}$
$\csc{\theta} =\dfrac{2\sqrt{3}}{3}$
$ \sec{\theta} =2$
$\cot{\theta} =\dfrac{\sqrt{3}}{3}$
Work Step by Step
$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$
$\therefore \tan{\theta}= \dfrac{\dfrac{\sqrt{3}}{2}}{\dfrac{1}{2}}=\sqrt{3}$
$\csc{\theta} = \dfrac{1}{\sin{\theta}}$
$\therefore \csc{\theta} = \dfrac{1}{\dfrac{\sqrt{3}}{2}}=\dfrac{2\sqrt{3}}{3}$
$\sec{\theta} = \dfrac{1}{\cos{\theta}}$
$\therefore \sec{\theta} = \dfrac{1}{\dfrac{1}{2}}= 2$
$\cot{\theta} = \dfrac{1}{\tan{\theta}}$
$\cot{\theta} = \dfrac{1}{\sqrt{3}}= \dfrac{\sqrt{3}}{3}$
