Chapter 4.1, Problem 16E

(a)

To determine

Find the angle $-\frac{\text{5π}}{12}$ lies in which quadrant.

Answer to Problem 16E

Fourth quadrant

Explanation of Solution

Given:

The angle $-\frac{\text{5π}}{12}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Negative angle measured in clockwise direction from the Horizontal axis. An angle   $-\frac{\text{5π}}{12}=-[\frac{\text{π}}{\text{2}}-\frac{\text{π}}{12}]$ => The angle is in the 4th Quadrant.

  $\frac{\text{3π}}{\text{2}}<-\frac{\text{5π}}{12}<2\text{π}$, so the angle $-\frac{\text{5π}}{12}$ lies in Fourth quadrant.

Thus, the angle $-\frac{\text{5π}}{12}$ lies in Fourth Quadrant.

(b)

To determine

Find the angle $-\frac{\text{13π}}{9}$ lies in which quadrant.

Answer to Problem 16E

second quadrant

Explanation of Solution

Given:

The angle $-\frac{\text{13π}}{9}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Negative angle measured in clockwise direction from the Horizontal axis An angle of   $-\frac{\text{13π}}{9}=-[\text{π}+\frac{\text{4π}}{9}]$ => The angle in in the 2nd Quadrant

  $\frac{\text{π}}{2}<-\frac{\text{13π}}{9}<\text{π}$, so the angle $-\frac{\text{13π}}{9}$ lies in second quadrant.

Thus, the angle $-\frac{\text{13π}}{9}$ lies in second Quadrant.