Question

draw the angle in standard position. state the quadrant in which the angle lies. work the exercise without converting to degrees. -\frac{11\pi}{6}
choose the correct graph below.

Explanation:

Step1: Add \(2\pi\) to the angle

Since \(2\pi=\frac{12\pi}{6}\), then \(-\frac{11\pi}{6}+ \frac{12\pi}{6}=\frac{\pi}{6}\). Adding \(2\pi\) to an angle does not change its terminal - side position.

Step2: Determine the quadrant

The angle \(\frac{\pi}{6}\) is between \(0\) and \(\frac{\pi}{2}\). Angles in the range \(0\lt\theta\lt\frac{\pi}{2}\) lie in the first quadrant.

Answer:

The angle \(-\frac{11\pi}{6}\) lies in the first quadrant. Without seeing the actual graphs, a first - quadrant angle has its terminal side in the region where \(x>0\) and \(y > 0\). If one of the graphs shows an angle with its terminal side in the first quadrant, that is the correct graph.