Which of the following is true of the location of an angle, \( \theta \), whose tangent value is \( -\frac{\sqrt{3}}{3} \) ? \( \theta \) has a 30 -degree reference angle and is located in Quadrant II or IV \( \theta \) has a 30 -degree reference angle and is located in Quadrant II or III \( \theta \) has a 60 -degree reference angle and is located in Quadrant II or IV \( \theta \) has a 60 -degree reference angle and is located in Quadrant II or III ?

The correct statement is that \( \theta \) has a 30-degree reference angle and is located in Quadrant II or IV. This is because tangent is negative in these quadrants, and a 30-degree reference angle means that the corresponding angles in these quadrants are \( 180^\circ - 30^\circ = 150^\circ \) for Quadrant II and \( 360^\circ - 30^\circ = 330^\circ \) for Quadrant IV. When dealing with trigonometric functions, it’s crucial to remember how angles behave across the four quadrants. The tangent function is positive in Quadrants I and III, while it’s negative in Quadrants II and IV. So, if you see \( \tan(\theta) = -\frac{\sqrt{3}}{3} \), you're looking for angles that sit snugly in those second and fourth quadrants with a 30-degree reference angle!