Answer
$\sin{\theta} = \dfrac{\sqrt{5}}{5}$
$\cos{\theta} =-\dfrac{2\sqrt{5}}{5} $
$\tan{\theta} =-\dfrac{1}{2}$
$\csc{\theta} =\sqrt{5}$
$\sec{\theta} =-\dfrac{\sqrt{5}}{2}$
$\cot{\theta} =-2$
Work Step by Step
$\sin{\theta} = \dfrac{y}{r} \hspace{20pt} \because \sin{\theta} > 0 \hspace{10pt}\therefore y$ is positive.
$ \tan{\theta} = \dfrac{y}{x} = -\dfrac{1}{2}$
$\therefore x = -2 \hspace{20pt} y = 1 \hspace{20pt} QII$
$r = \sqrt{x^2+y^2} = \sqrt{(1)^2+(-2)^2} = \sqrt{5}$
$\sin{\theta} = \dfrac{y}{r} = \dfrac{\sqrt{5}}{5}$
$\cos{\theta} = \dfrac{x}{r} = -\dfrac{2\sqrt{5}}{5} $
$\csc{\theta} = \dfrac{1}{\sin{\theta}} = \sqrt{5}$
$\sec{\theta} = \dfrac{1}{\cos{\theta}} = -\dfrac{\sqrt{5}}{2}$
$\cot{\theta} = \dfrac{1}{\tan{\theta}} = -2$
