Chapter 4.1, Problem 35E

(a)

To determine

Find the angle $132.50\text{'}$ lies in which quadrant.

Answer to Problem 35E

Second Quadrant

Explanation of Solution

Given: The angle $132.50\text{'}$

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:

Converting the minutes into degree.

We know that: $\begin{array}{l}{1}^0=60\text{'}\\ 50\text{'}={\frac{50}{60}}^0={0.8}^0\\ {132}^{0}50\text{'}={132.8}^0\end{array}$

  ${90}^0<{132.8}^0<{180}^0$; The angle $132.50\text{'}$ lies in the Second quadrant.

Thus, the angle $132.50\text{'}$ lies in the Second quadrant.

(b)

To determine

Find the angle $-{336}^{0}30\text{'}$ lies in which quadrant.

Answer to Problem 35E

First Quadrant

Explanation of Solution

Given: The angle $-{336}^{0}30\text{'}$

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:

Converting the minutes into deg.

We know that: $\begin{array}{l}{1}^0=60\text{'}\\ 30\text{'}={\frac{30}{60}}^0={0.5}^0\\ -{336}^{0}30\text{'}=-{336.5}^0\end{array}$

A Negative angle measured in clockwise direction from the Horizontal axis .

Thus, theangle $-{336}^{0}30\text{'}$ lies in FirstQuadrant.