Given:
[tex]v=<5,-2>[/tex]To Determine: The direction angle in the interval [0 degree, 360 degrees)
Solution
Given
[tex]\begin{gathered} \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]Substitute
Note that the vector is in the fourth quadrant
[tex]\begin{gathered} \theta=tan^{-1}(-\frac{2}{5}) \\ \theta=tan^{-1}(-0.4) \\ \theta=-(21.80^0) \\ \theta=360-21.80 \\ \theta=338.20^0 \end{gathered}[/tex]Hence, the direction angle is 338.20⁰
