Answer
Horizontal component $=-458.88$
Vertical component $=655.36$
$\vec{v}=-458.88\vec{i}+655.36\vec{j}$
Work Step by Step
$|\vec{v}|=800$ $,$ $\theta=125^{\circ}$
Multiply the magnitude of the vector $\vec{v}$ by the cosine of $\theta$ to obtain its horizontal component:
Horizontal component:
$|\vec{v}|\cos\theta=800\cos125^{\circ}\approx800(-0.5736)\approx-458.88$
Multiply the magnitude of the vector $\vec{v}$ by the sine of $\theta$ to obtain its vertical component:
Vertical component:
$|\vec{v}|\sin\theta=800\sin125^{\circ}\approx800(0.8192)\approx655.36$
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 $\vec{j}$:
$\vec{v}=-458.88\vec{i}+655.36\vec{j}$
