Answer
$\sin{\theta} =\dfrac{2\sqrt{5}}{5}$
$\cos{\theta} = \dfrac{\sqrt{5}}{5}$
Work Step by Step
$y = 2x \\ \therefore \dfrac{y}{x} = 2 \\ \because \tan{\theta} = \dfrac{y}{x} \\ \therefore \tan{\theta} = 2$
$\because$ The terminal side of $\theta$ lies in $QI%$, then $x$ and $y$ are both positive.
$ \therefore$ Let $y=2$ and $x =1$
$r = \sqrt{x^2+y^2} = \sqrt{1^2+2^2} = \sqrt{5}$
$\sin{\theta} = \dfrac{y}{r} = \boxed{\dfrac{2\sqrt{5}}{5}}$
$\cos{\theta} = \dfrac{x}{r} = \boxed{\dfrac{\sqrt{5}}{5}}$
