Chapter 4.1, Problem 52E

(a)

To determine

Convert $-4\text{π}$ radian in degrees.

Answer to Problem 52E

  $-720\text{Degree}$

Explanation of Solution

Given:

The angle $-4\text{π}$ radian

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

Calculation:

  $\begin{array}{l}\text{π}\text{radian}={180}^0\\ 1\text{radian}=\frac{\text{180}}{\text{π}}\text{Degree}\\ -4\text{π}\text{radian}=-4\text{π}·\frac{\text{180}}{\text{π}}\text{Degree}=-720\text{Degree}\end{array}$

Thus, $-4\text{π}\text{radian}$ is equivalent to $-720\text{Degree}$

(b)

To determine

Convert $3\text{π}\text{radian}$ in Degree.

Answer to Problem 52E

  $540\text{Degree}$

Explanation of Solution

Given:

The angle $3\text{π}\text{radian}$

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

Calculation:

  $\begin{array}{l}\text{π}\text{radian}={180}^0\\ 1\text{radian}=\frac{\text{180}}{\text{π}}\text{Degree}\\ 3\text{π}\text{radian}=3\text{π}·\frac{\text{180}}{\text{π}}\text{Degree}=540\text{Degree}\end{array}$

Thus, $3\text{π}\text{radian}$ is equivalent to $540\text{Degree}$