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 magnitude of the horizontal and vertical components (using the grid). If we consider the right - triangle formed by the vector's components, we can find the reference angle. For a vector in the third quadrant, if we assume the horizontal component \(x=- 2\) and vertical component \(y = - 4\) (approximate from the grid). The reference angle \(\theta_{r}\) is given by \(\tan\theta_{r}=\frac{\vert y\vert}{\vert x\vert}\). Here \(\tan\theta_{r}=\frac{4}{2} = 2\), so \(\theta_{r}\approx63^{\circ}\)

Step2: Calculate the direction angle

The formula for the direction angle \(\theta\) of a vector in the third quadrant is \(\theta = 180^{\circ}+\theta_{r}\). Substituting \(\theta_{r}\approx63^{\circ}\), we get \(\theta=180^{\circ}+ 63^{\circ}=243^{\circ}\)

Answer:

D. 243°