Chapter 4.1, Problem 31E

(a)

To determine

Find the angle ${55}^0$ lies in which quadrant.

Answer to Problem 31E

First quadrant

Explanation of Solution

Given: The angle ${55}^0$

Concept Used:

Quadrants are usually denoted by roman letters I, II, III and IV as shown in the figure below:

• Angles between 0° and 90° are in the first quadrant.
• Angles between 90° and 180° are in the second quadrant.
• Angles between 180° and 270° are in the third quadrant.
• Angles between 270° and 360° are in the fourth quadrant.

Calculation:

  $0^0<{55}^0<{90}^0$; theangle ${55}^0$ lies in First Quadrant.

Thus, theangle ${55}^0$ lies in First Quadrant.

(b)

To determine

Find the angle ${215}^0$ lies in which quadrant.

Answer to Problem 31E

Third Quadrant

Explanation of Solution

Given: The angle ${215}^0$

Concept Used:

Quadrants are usually denoted by roman letters I, II, III and IV as shown in the figure below:

• Angles between 0° and 90° are in the first quadrant.
• Angles between 90° and 180° are in the second quadrant.
• Angles between 180° and 270° are in the third quadrant.
• Angles between 270° and 360° are in the fourth quadrant.

Calculation:

  ${180}^0<{215}^0<{270}^0$; the angle ${215}^0$ lies in the third quadrant.

Thus, the angle ${215}^0$ lies in the third quadrant.