## Precalculus (10th Edition)

$333.43^\circ.$
If $v=ai+bj$ then by definition $tan(\alpha)=\frac{b}{a}$, hence $\alpha=tan^{-1}(\frac{b}{a})$. Also $0^\circ\lt\alpha\lt360^\circ.$ Therefore here $\alpha=tan^{-1}(\frac{-2}{4})=tan^{-1}(-0.5)=333.43^\circ.$ (because it must be in Quadrant IV).