Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$225^{\circ}$
Let us consider that a vector $v$ is given by $v=pi+qj$ and makes an angle of $\alpha$ with the positive $x$-axis. The direction angle $\alpha$ for the given vector can be determined using the formula: $\tan \alpha=\dfrac{q}{p}$ Here, we have: $v=-5 i -5 j$ Now, $\tan \alpha=\dfrac{ -5}{-5}=1$ Which gives $\alpha=45^{\circ}$. Since the angle must be in the 3rd quadrant, then the direction angle is: $\alpha=\arctan (1)=225^{\circ}$