Chapter 4.1, Problem 15E

(a)

To determine

Find the angle $\frac{\text{7π}}{\text{4}}$ lies in which quadrant.

Answer to Problem 15E

First Quadrant.

Explanation of Solution

Given:

The angle $\frac{\text{7π}}{\text{4}}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Positive angle measured in counter clockwise direction. a) An angle of   $\frac{\text{7π}}{\text{4}}$ is lies in the 4th quadrant.

  $\frac{\text{3π}}{\text{2}}<\frac{\text{7π}}{\text{4}}<\text{π}$, so the angle $\frac{\text{7π}}{\text{4}}$ lies in fourth quadrant.

Thus, the angle $\frac{\text{7π}}{\text{4}}$ lies in Fourth Quadrant.

(b)

To determine

Find the angle $\frac{\text{11π}}{\text{4}}$ lies in which quadrant.

Answer to Problem 15E

Secondquadrant

Explanation of Solution

Given:

The angle $\frac{\text{11π}}{\text{4}}$ lies in which quadrant.

Concept Used:

  

Calculation:

A Positive angle measured in counter clockwise direction. b) An angle   $\frac{\text{11π}}{4}=2\text{π}+\frac{\text{3π}}{4}$ lies is in the 2nd quadrant.

  $\frac{\text{π}}{2}<\frac{\text{11π}}{4}<\text{π}$, so the angle $\frac{\text{11π}}{\text{4}}$ lies in second quadrant.

Thus, the angle $\frac{\text{11π}}{\text{4}}$ lies in Second Quadrant.