Chapter 4.1, Problem 11E

a.

To determine

Tofind:The quadrant in which the angle $\frac{\pi }{4}$ lies.

Answer to Problem 11E

The angle $\frac{\pi }{4}$ lies in Quadrant I.

Explanation of Solution

Given information:

The give angle is $\frac{\pi }{4}$ .

Calculation:

The angle $\frac{\pi }{4}$ is greater than 0 but less than $\frac{\pi }{2}$ . So, the angle ranges between $0<\frac{\pi }{4}<\frac{\pi }{2}$ .

Therefore, the angle $\frac{\pi }{4}$ lies in Quadrant I.

b.

To determine

Tofind:The quadrant in which the angle $-\frac{5\pi }{4}$ lies.

Answer to Problem 11E

The angle $-\frac{5\pi }{4}$ lies in Quadrant II.

Explanation of Solution

Given information:

The give angle is $-\frac{5\pi }{4}$ .

Calculation:

The angle $-\frac{5\pi }{4}$ is conterminal with $\frac{3\pi }{4}$ and it ranges between $\frac{\pi }{2}<\frac{3\pi }{4}<\pi$ .Therefore, the angle $-\frac{5\pi }{4}$ lies in Quadrant II.