Chapter T, Problem 1DDT

(a)

To determine

To convert: The value $300°$ into radians.

Answer to Problem 1DDT

The value $300°$ is equal to $\frac{5}{3}\text{π}$ radians.

Explanation of Solution

Formula used:

Relation between degree and radians: $\text{radians}=\text{degree×}\frac{\text{π}}{\text{180°}}$.

Calculation:

Consider the given degree $300°$.

Use the above mentioned formula and compute $300°$ to radians as follows,

$\begin{array}{c}\text{radians}=\text{300}°\text{×}\frac{\text{π}}{\text{180°}}\\ =\frac{30}{18}\text{π}\\ \text{=}\frac{5}{3}\text{π}\end{array}$

Thus, The value $300°$ is equal to $\frac{5}{3}\text{π}$ radians.

(b)

To determine

To convert: The value $-18°$ into radians.

Answer to Problem 1DDT

The value $-18°$ is equal to $-\frac{1}{10}\text{π}$ radians.

Explanation of Solution

Formula used:

Relation between degree and radians: $\text{radians}=\text{degree×}\frac{\text{π}}{\text{180°}}$.

Calculation:

Consider the given degree $-18°$.

Use the above mentioned formula and compute $-18°$ to radians as follows,

$\begin{array}{c}\text{radians}=-18°\text{×}\frac{\text{π}}{\text{180°}}\\ =-\frac{18}{180}\text{π}\\ \text{=}-\frac{1}{10}\text{π}\end{array}$

Thus, the value $-18°$ is equal to $-\frac{1}{10}\text{π}$ radians.