Answer
$\cos{x}=\dfrac{\sqrt{5}}{5}$
$\sin{x} = \dfrac{2\sqrt{5}}{5}$
Work Step by Step
Since $x$ lies in the first quadrant, $\sin{x}$ and $\cos{x}$ are positive.
Using the formula:
$$\sec{x}=\sqrt{1+\tan^2{x}}$$
$$\sec{x}=\sqrt{1+(2)^2}$$
$$\sec{x}=\sqrt{5}$$
$\because \cos{x}=\dfrac{1}{\sec{x}}$
$\therefore \cos{x}=\dfrac{1}{\sqrt{5}} = \dfrac{\sqrt{5}}{5}$
Using the formula:
$$\sin{x}=\sqrt{1-\cos^2{x}}$$
$$\sin{x}=\sqrt{1-\left( \dfrac{\sqrt{5}}{5}\right)^2}$$
$$\sin{x} = \dfrac{2\sqrt{5}}{5}$$
