Question

review the graph.
what is the approximate direction angle of the vector shown?
○ 27°
○ 63°
○ 207°
○ 243°

Explanation:

Step1: Determine the reference angle

The vector is in the third - quadrant. Let's assume the vector has components \(x=-2\) and \(y = - 1\). The reference angle \(\theta_{r}\) is given by \(\tan\theta_{r}=\frac{\vert y\vert}{\vert x\vert}\). So, \(\tan\theta_{r}=\frac{1}{2}\approx0.5\). Using the inverse - tangent function \(\theta_{r}=\tan^{- 1}(0.5)\approx27^{\circ}\).

Step2: Calculate the direction angle in the third - quadrant

The formula for the direction angle \(\theta\) of a vector in the third - quadrant is \(\theta = 180^{\circ}+\theta_{r}\). Substituting \(\theta_{r}\approx27^{\circ}\), we get \(\theta=180^{\circ}+27^{\circ}=207^{\circ}\).

Answer:

\(207^{\circ}\)