Chapter 50, Problem 8A

To determine

(a)

The number of degrees present in 1 circle.

Answer to Problem 8A

The number of degrees present in 1 circle is 360 degree $\left(360°\right)$.

Explanation of Solution

There are 360 degree in 1 circle.

To determine

(b)

The total number of minutes in 1degree.

Answer to Problem 8A

  $\text{1}\text{Degree}\left(\text{°}\right)=60\text{Minutes}\left({}^{\prime }\right)$.

Explanation of Solution

A degree is divided into 60-parts called as minutes.

  $\text{1}\text{Degree}\left(\text{°}\right)=60\text{Minutes}\left({}^{\prime }\right)$.

So, the total number of minutes in 1-degree is 60.

To determine

(c)

The total number of seconds in 1 minute.

Answer to Problem 8A

  $1\text{Minutes}\left({}^{\prime }\right)=60\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)$.

Explanation of Solution

  $\begin{array}{l}\text{1Circle}=360\text{Degree}\left(\text{°}\right)\\ \text{1}\text{Degree}\left(\text{°}\right)=60\text{Minutes}\left({}^{\prime }\right)\\ 1\text{Minutes}\left({}^{\prime }\right)=60\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)\end{array}$

A minute is divided into 60-parts called as second.

So, the total number of seconds in 1minute is 60.

To determine

(d)

The total number of seconds in 1-degree.

Answer to Problem 8A

The total number of seconds in 1-degree is $360\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)$.

Explanation of Solution

  $\begin{array}{l}\text{1}\text{Degree}\left(\text{°}\right)=60\text{Minutes}\left({}^{\prime }\right)\\ \because 1\text{Minutes}\left({}^{\prime }\right)=60\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)\\ \text{Therefore,}\\ \text{1}\text{Degree}\left(\text{°}\right)=60\left[60\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)\right]\\ \text{1}\text{Degree}\left(\text{°}\right)=60\times 60\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)=3600\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)\end{array}$

so, total number of seconds in 1-degree is $3600\text{Seconds}\left({{}^{\prime }}^{\prime \text{}}\right)$.

To determine

(e)

The total number of minutes in 1-circle.

Answer to Problem 8A

The total number of minutes in 1-circle is $21600\text{Minutes}\left({}^{\prime }\right)$.

Explanation of Solution

  $\begin{array}{l}\text{1Circle}=360\text{Degree}\left(\text{°}\right)\\ \because \text{1}\text{Degree}\left(\text{°}\right)=60\text{Minutes}\left({}^{\prime }\right)\\ \text{Therefore,}\\ \text{1Circle}=360\left[\text{1Degree}\left(\text{°}\right)\right]\\ \text{1Circle}=360\left[60\text{Minutes}\left({}^{\prime }\right)\right]=21600\text{Minutes}\left({}^{\prime }\right)\end{array}$

So, the total number of minutes in 1-circle is $21600\text{Minutes}\left({}^{\prime }\right)$.