Chapter 4.1, Problem 17E

(a)

To determine

Find the angle − 1 radian lies in which quadrant.

Answer to Problem 17E

Fourth Quadrant

Explanation of Solution

Given:

The angle − 1 radian

Concept Used:A negative angle is counted clockwise direction from the Horizontal axis.

We know that:

Q1 from $\text{0}\text{to}\frac{\text{π}}{\text{2}}$ = 1.5708 radians.

Q2 is from $\frac{\text{π}}{\text{2}}$ = 1.5708 to $\text{π}$ = 3.1416 radians.

Q3 is from $\text{π}$ = 3.1416 to $\frac{\text{3π}}{\text{2}}$ = 4.7125 radians and

Q4 is from $\frac{\text{3π}}{\text{2}}$ = 4.7124 to $\text{2π}$ = 6.2832 radians.

Calculation:

−1 radian is equivalent to − 1 + $\text{2π}$ = − 1 + 6.2832 = 5.2832 radians.

Hence − 1 radian lies in Q4.

Thus, − 1 radian lies in Fourth Quadrant

(b)

To determine

Find the angle − 2 radianslies in which quadrant.

Answer to Problem 17E

Third Quadrant

Explanation of Solution

Given:

The angle − 2 radians

Concept Used: A negative angle is counted clockwise direction from the Horizontal axis.

We know that:

Q1 from $\text{0}\text{to}\frac{\text{π}}{\text{2}}$ = 1.5708 radians.

Q2 is from $\frac{\text{π}}{\text{2}}$ = 1.5708 to $\text{π}$ = 3.1416 radians.

Q3 is from $\text{π}$ = 3.1416 to $\frac{\text{3π}}{\text{2}}$ = 4.7125 radians and

Q4 is from $\frac{\text{3π}}{\text{2}}$ = 4.7124 to $\text{2π}$ = 6.2832 radians.

Calculation:

−2 radian is equivalent to − 2 + $\text{2π}$ = − 2 + 6.2832 = 4.2832 radians.

Hence − 2 radians lies in Q3.

Thus, − 2 radians lies in Third Quadrant