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