How do you find the remaining trigonometric functions of theta given tantheta=-1/2 and sintheta>0?

$\tan t = - \frac{1}{2} - \to \cot t = - 2$
${\sin}^{2} t = \frac{1}{1 + {\cot}^{2} t} = \frac{1}{1 + 4} = \frac{1}{5}$
$\sin t = \pm \frac{1}{\sqrt{5}} = = \pm \frac{\sqrt{5}}{5}$
${\cos}^{2} t = 1 - {\sin}^{2} t = 1 - \frac{1}{5} = \frac{4}{5}$
$\cos t = \pm \frac{2}{\sqrt{5}}$
$\sec t = \frac{1}{\cos} = - \frac{\sqrt{5}}{2}$
$\csc t = \frac{1}{\sin} = \sqrt{5}$