Chapter 4.1, Problem 12E

a.

To determine

Find the quadrant for the given angle.

Answer to Problem 12E

The given angle lies in the fourth quadrant.

Explanation of Solution

Given:

The given angle is $-\frac{\pi }{6}$ .

Calculation:

An angle is determined by rotating a ray (half-line) about its endpoint. The starting position of the ray is the initial side of the angle, and the position after rotation is the terminal side. In standard position, counterclockwise rotation of ray represents the positive angle and clockwise represents negative angle.

Now

  $-\frac{\pi }{6}=-\frac{180}{6}=-{30}^{°}$

  $-{30}^{°}$ is a negative angle (clockwise direction). Its present in the fourth quadrant.

  

Hence the given angle lies in the fourth quadrant.

b.

To determine

Find the quadrant for the given angle.

Answer to Problem 12E

The given angle lies in the first quadrant.

Explanation of Solution

Given:

The given angle is $-\frac{11\pi }{6}$ .

Calculation:

An angle is determined by rotating a ray (half-line) about its endpoint. The starting position of the ray is the initial side of the angle, and the position after rotation is the terminal side. In standard position, counterclockwise rotation of ray represents the positive angle and clockwise represents negative angle.

Now

  $\begin{array}{l}-\frac{11\pi }{6}\\ =-\frac{11\times 180}{6}\\ =-11\times {30}^{°}\\ =-{330}^{°}\end{array}$

  $-{330}^{°}={360}^{°}-{330}^{°}={30}^{°}$

  ${30}^{°}$ is a positive angle (counterclockwise direction). Its present in the first quadrant.

  

Hence the given angle lies in the first quadrant.