Answer
$\boldsymbol{v}=\langle2,2\sqrt{3}\rangle$.
Work Step by Step
$\boldsymbol{v}=\langle a_{1},a_{2}\rangle$. If we think of the vector as a triangle with a hypotenuse of $4$, we can use trigonometry to find the components of $\boldsymbol{v}$.
$a_{1}=4\cos{\frac{\pi}{3}}=\frac{4}{2}=2\Rightarrow a_1=2$
$a_{2}=4\sin{\frac{\pi}{3}}=\frac{4\sqrt{3}}{2}=2\sqrt{3}\Rightarrow a_2=2\sqrt{3}$
