Answer
Horizontal component $=3.9392$
Vertical component $=0.6944$
$\vec{v}=3.9392\vec{i}+0.6944\vec{j}$
Work Step by Step
$|\vec{v}|=4$ $,$ $\theta=10^{\circ}$
Multiply the magnitude of the vector $\vec{v}$ by the cosine of $\theta$ to obtain its horizontal component:
Horizontal component
$|\vec{v}|\cos\theta=4\cos10^{\circ}\approx4(0.9848)\approx3.9392$
Multiply the magnitude of the vector $\vec{v}$ by the sine of $\theta$ to obtain its vertical component:
Vertical component
$|\vec{v}|\sin\theta=4\sin10^{\circ}\approx4(0.1736)\approx0.6944$
Write the vector in terms of $\vec{i}$ and $\vec{j}$. Do so by adding the product between its horizontal component and $\vec{i}$ and the product between its vertical component and $\vec{j}$:
$\vec{v}=3.9392\vec{i}+0.6944\vec{j}$
