Answer
$\sin{\theta} =-\dfrac{1}{2}$
$\cos{\theta} =\dfrac{\sqrt{3}}{2}$
$\tan{\theta}=-\dfrac{\sqrt{3}}{3}$
$\csc{\theta} =-2$
$\sec{\theta} = \dfrac{2\sqrt{3}}{3}$
$\cot{\theta} =-\sqrt{3}$
Work Step by Step
From figure 22, the coordinates of $\dfrac{11\pi}{6}$ on the unit circle are $\left(\dfrac{\sqrt{3}}{2},-\dfrac{1}{2}\right)$
$\cos{\theta} = \text{x-coordinate } = \dfrac{\sqrt{3}}{2}$
$\sin{\theta} = \text{y-coordinate } = -\dfrac{1}{2}$
$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}} = -\dfrac{\sqrt{3}}{3}$
$\csc{\theta} = \dfrac{1}{\sin{\theta}} = -2$
$\sec{\theta} = \dfrac{1}{\cos{\theta}} = \dfrac{2\sqrt{3}}{3}$
$\cot{\theta} =\dfrac{1}{\tan{\theta}} = -\sqrt{3}$
