[tex]\bf u=-3i+8j\implies u=\ \textless \ \stackrel{a}{-3}~~,~~\stackrel{b}{8}\ \textgreater \ ~~
\begin{cases}
tan(\theta )=\frac{b}{a}\\\\
\measuredangle \theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}
\\\\\\
\measuredangle \theta =tan^{-1}\left(-\frac{8}{3} \right)\implies \measuredangle \theta \approx -69.44^o[/tex]
however, the x-coordinate is negative and the y-coordinate is positive, meaning the IV quadrant, namely 180° - 69°, or ≈ 111°.
