Question

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

Explanation:

Step1: Recall range of quadrants in radians

The range of the fourth - quadrant is \( \frac{3\pi}{2}<\theta < 2\pi\).

Step2: Rewrite the given angle

We can rewrite \(\frac{11\pi}{6}\) as \(2\pi-\frac{\pi}{6}\). Since \(2\pi = \frac{12\pi}{6}\), and \(\frac{3\pi}{2}=\frac{9\pi}{6}\), and \(\frac{9\pi}{6}<\frac{11\pi}{6}<\frac{12\pi}{6}\), the angle \(\frac{11\pi}{6}\) lies in the fourth - quadrant. In standard position, an angle in the fourth - quadrant has its terminal side in the fourth - quadrant.

Answer:

The angle \(\frac{11\pi}{6}\) lies in the fourth - quadrant. Without seeing the actual graphs, a correct graph of an angle \(\frac{11\pi}{6}\) in standard position would have the initial side on the positive \(x\) - axis and the terminal side in the fourth - quadrant.