Chapter 4.1, Problem 14E

(a)

To determine

The quadrant in which the angle $\frac{\text{5π}}{6}$ lies.

Answer to Problem 14E

Quadrant II

Explanation of Solution

Given:

The angle $\frac{\text{5π}}{6}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Positive angle measured in counter clockwise direction. a) An angle of $\frac{\text{5π}}{6}$ is in the 2nd quadrant.

  $\frac{\text{π}}{2}<\frac{\text{5π}}{6}<\text{π}$, so the angle $\frac{\text{5π}}{6}$ lies in second quadrant.

Thus, the angle $\frac{\text{5π}}{6}$ lies in second Quadrant.

(b)

To determine

Find the angle $-\frac{\text{5π}}{3}$ lies in which quadrant.

Answer to Problem 14E

First quadrant.

Explanation of Solution

Given:

The angle $-\frac{\text{5π}}{3}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Negative angle measured in clockwise direction from the Horizontal axis . An angle of   $-\frac{\text{5π}}{3}$ is in the first quadrant.

  $0<-\frac{\text{5π}}{3}<\frac{\text{π}}{2}$, so the angle $-\frac{\text{5π}}{3}$ lies in first quadrant.

Thus, the angle $-\frac{\text{5π}}{3}$ lies in first Quadrant.