Answer
$\cos{\theta} =\dfrac{1}{2}$
$\sin{\theta} =- \dfrac{\sqrt{3}}{2}$
$\tan{\theta}=-\sqrt{3}$
$\csc{\theta} =-\dfrac{2 \sqrt{3} }{3}$
$\cot{\theta} = -\dfrac{\sqrt{3}}{3}$
Work Step by Step
$\cos{\theta} = \dfrac{1}{\sec{\theta}} = \dfrac{1}{2}$
Since $\sin{\theta} <0$, then $\sin{\theta} = -\sqrt{1-\cos^2 {\theta}}$.
Thus,
$\sin{\theta} = -\sqrt{1-\left(\dfrac{1}{2} \right)^2}\\
=-\sqrt{\dfrac{4}{4}-\dfrac{1}{4}}\\
=-\sqrt{\dfrac{3}{4}}\\
= - \dfrac{\sqrt{3}}{2}$
$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$
$\tan{\theta}= \dfrac{- \dfrac{\sqrt{3}}{2}}{\dfrac{1}{2}} = -\sqrt{3}$
$\csc{\theta} = \dfrac{1}{\sin{\theta}}$
$\csc{\theta} = \dfrac{1}{- \dfrac{\sqrt{3}}{2}}= -\dfrac{2 \sqrt{3} }{3}$
$\cot{\theta} = \dfrac{1}{\tan{\theta}}$
$\cot{\theta} = \dfrac{1}{-\sqrt{3}} = -\dfrac{\sqrt{3}}{3}$
