Chapter 4.1, Problem 12E

a.

To determine

TO-DETERMINE the quadrant in which each angle lies.

Answer to Problem 12E

The angle $-\frac{\pi }{6}$ lies in quadrant $\text{IV}$ .

Explanation of Solution

Given information:

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

Calculation:

The angle $-\frac{\pi }{6}$ is negative that means angle rotate in clockwise direction.

Each quadrant represents the change of $\frac{\pi }{2}\text{radian}$ .

From the above diagram.

The angle $-\frac{\pi }{6}$ lies in quadrant $\text{IV}$ .

b.

To determine

TO-DETERMINE the quadrant in which each angle lies.

Answer to Problem 12E

The angle $\frac{11\pi }{9}$ lies in quadrant $\text{III}$ .

Explanation of Solution

Given information:

The angle is $\frac{11\pi }{9}$ .

Calculation:

Convert $\frac{11\pi }{9}$ in degree.

  $\begin{array}{l}\frac{11\pi }{9}\text{radian=}\left(\frac{11\pi }{9}\text{radian}\right)\left(\frac{180}{\pi }\cdot \frac{\text{degree}}{\text{radian}}\right)\\ \frac{11\pi }{9}\text{radian=}\left(\frac{11\pi }{9}\cdot \frac{180}{\pi }\right)\left(\text{radian}\cdot \frac{\text{degree}}{\text{radian}}\right)\end{array}$

Cancel out common terms.

  $\begin{array}{c}\frac{11\pi }{9}\text{radian=}\left(\frac{11}{1}\cdot \frac{20}{1}\right)\left(\text{radian}\cdot \frac{\text{degree}}{\text{radian}}\right)\\ \frac{11\pi }{9}\text{radian=220}\text{degree}\\ \frac{11\pi }{9}=220°\end{array}$

The angle $220°$ is positive that means angle rotate in anticlockwise direction.

Each quadrant represents the change of $90°$ .

From the above diagram.

So, the angle $220°$ passes through the quadrants $\text{I,}\text{II}$ , and end in quadrant $\text{III}$ .

The angle $220°$ lies in quadrant $\text{III}$ .