Chapter 4.1, Problem 49E

(a)

To determine

Convert ${18}^0$ in radian.

Answer to Problem 49E

  $\frac{\text{π}}{10}\text{radian}$

Explanation of Solution

Given:

The angle ${18}^0$

Concept Used:

Radian is a unit of measure for angles.One radian is the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle.

The Relation between Degrees and Radians is ${180}^0=\text{π}\text{radian}$

Calculation:

  $\begin{array}{l}{180}^0=\text{π}\text{radian}\\ 1^0=\frac{\text{π}}{180}\text{radian}\\ {18}^0=18·\frac{\text{π}}{180}\text{radian}\text{=}\frac{\text{18π}}{180}\text{radian}\text{=}\frac{\text{π}}{10}\text{radian}\end{array}$

Thus, ${18}^0$ is equivalent to $\frac{\text{π}}{10}\text{radian}$

(b)

To determine

Convert $-{240}^0$ in radian.

Answer to Problem 49E

  $-\frac{\text{4π}}{3}\text{radian}$

Explanation of Solution

Given:

The angle $-{240}^0$

Concept Used:

Radian is a unit of measure for angles.One radian is the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle.

The Relation between Degrees and Radians is ${180}^0=\text{π}\text{radian}$

Calculation:

  $\begin{array}{l}{180}^0=\text{π}\text{radian}\\ 1^0=\frac{\text{π}}{180}\text{radian}\\ -{240}^0=-240·\frac{\text{π}}{180}\text{radian}\text{=}-\frac{\text{240π}}{180}\text{radian}\text{=}-\frac{\text{4π}}{3}\text{radian}\end{array}$

Thus, $-{240}^0$ is equivalent to $-\frac{\text{4π}}{3}\text{radian}$