Contents

**Minute Angle|Definition & Meaning**

**Definition**

A second is 1/3600 of a degree. Three hundred and sixty **degrees **make a whole **circle**. Each of the **sixty** sections that make up each degree is **1/60th** of a **degree**. These sections are known as **minutes**. A **minute **is divided into 60 equal **sections**, each of which is **1/60th **of a **minute**. These sections are termed **seconds**.

Three hundred and sixty **degrees **are contained in a whole **circle**. Each of the **sixty** sections that make up each degree is **1/60th** of a **degree**. These sections are known as **minutes**.

A **minute **is divided into 60 equal **sections**, each of which is **1/60th **of a **minute**. These sections are termed **seconds**.

Figure 1: A minute angle is extremely small. This is a zoomed-in version of the minute angle expressed on a circle.

The use of the terms **minute **and **second **here has nothing to do with how those terms are typically used to refer to **time periods**.

1 degree = 60’

1 minute = 60’’

1 degree = 3600’’

**Reason for Converting Degrees Into Minutes**

Because **hours **are split into **minutes **and minutes are further divided into **seconds**, how will you claim that it is neither five o’clock nor six o’clock? Simply mention it, for instance, 20 past five.

Similar to how **minutes **and **seconds **are used to divide **angles**, minutes and seconds are used to assist you to explain that an angle may not be **100 degrees** or **105 degrees** but anything in between them, for instance, **100 degrees 45 minutes** is equivalent to **100.75 **degrees.

**Using ** **D°M’S’’ Locating Coordinates on the Globe**

Using **latitude **and **longitude**, we can locate any place on the planet for **positioning**. These **coordinates **are measured in **decimal **degrees or **D°M’S’’**. **Longitude **coordinates can be divided between **-180 **and **+180 **degrees, whereas **latitude **lines span between **-90 **and **+90 **degrees.

Any point on **Earth **can be identified by its **longitude **and **latitude **using a **geographic coordinate system **(GCS). We utilize **angles **expressed in degrees or more precisely, **D°M’S’’** from the earth’s **center **to any point on its surface since a **GCS **employs a **sphere **to describe **locations **on the planet.

The **intersection **of the **equator **and **Prime Meridian **is at the coordinates (0°0’0’’N, 0°0’0’’E) which is amusingly just all ocean.

**Positions **are generally expressed in **degrees**, **minutes**, and **seconds **of angles for two measurements: **latitude**, which is the angle **north **or **south **of the **equator**, and **longitude**, which refers to the angle **east **or **west **of the **Prime Meridian**.

Using degrees-minutes-seconds **(D°M’S’)** is one technique to represent **spherical coordinates **(**latitudes **and **longitudes**). The span of **minutes **and **seconds **is 0 to 60. For instance, the **geographic coordinates **of Paris are as follows when stated in **degrees-minutes-seconds**:

Latitude: 48 degrees, 51 minutes, 52.97 seconds N

Longitude: 2 degrees, 20 minutes, 52.97 seconds E

However, **decimal **degrees can also be used to indicate **geographic coordinates**. It’s just another **format **in which one can portray the same **location**. Here is the city of Paris, for instance, expressed in **decimal **degrees:

Latitude: 48.864716 N

Longitude: 2.349014 E

**Importance and Relation With Time**

The **year **was thought to be roughly **360 **days long in the early days of human history. They lacked **accurate **measuring **equipment**, but it was simple enough just to add a **month **every **six **years or so until they became aware of the accumulating **change**.

We owe the concept of **360 degrees **in a circle to the Babylonians since it was a discernible **cycle **that led to the idea that a **circle **should have that many **segments**. It was easy to divide **360 **into many different numbers, making it a useful number.

They divided each **degree **into **60-minute **increments in order to achieve more **accuracy**. They quickly needed even greater **accuracy**, so they separated every **minute **into a **second**, the second order minute. Babylonian trigonometry is still in use today.

As transportable and precise clocks proliferated, it was clear that the **position **of the sun varied around the globe. By comparing the **position **of the sun or stars to a reference **time**, we were able to determine our location.

However, a **degree **is a rather significant **distance**. A **degree **of **arc** at the **equator **is **1/360** of a **circumference **of around **25000 **miles (actually 24901). As a result, **69.17 **miles are equal to one **degree **of arc. That equates to around **365,215 **feet.

The result of dividing that by **60 **is approximately 6087 feet. One **degree **of arc is equivalent to one sea mile since it is about **15%** longer than a standard mile (**5280** feet).

**Examples Explaining the Concept of Degrees, Minutes, and Seconds**

**Example 1**

Convert 125.45° degrees into D°M’S” form.

**Solution**

As we are aware that 1 degree is equal to 60’ and 1 minute is equal to 60’’, so let us use this to calculate the required result.

First, we have to split the whole number and the decimal parts:

125.45° = 125° + 0.45°

= (125°) + (45/100°)

= (125°) + (9/20°)

Multiplying 9/20 by 1°:

= (125°) + (9/20 .1°)

As 1° = 60’:

= (125°) + (9/20 .60’)

= (125°) + (9×3’)

Or:

= 125° + 27’

Now adding the seconds part:

= 125° + 27’ + 0’’

The conversion results in:

= 125° 27’ 0’’

Hence, the decimal has been converted into D°M’S” form.

**Example 2**

Convert 30°15’10’’ into decimal notation.

**Solution**

In the first step, let us split the D°M’S’’ notation into parts:

= 30° + 15’ + 10’’

We can write the above expression as:

= 30° + 15. 1’ + 10.1’’

Now, as 1’ = 1/60° and 1’’ = 1/3600°, let us plug in their values in the above expression:

= 30° + 15. 1/60° + 10.1/3600°

= 30° + 0.25° + 0.0027°

= 30.2527°

**Example 3**

Convert 45°30’20’’ into radians.

**Solution**

We will have to convert the above expression into degree notation first. We will follow the same pattern s we did previously.

Let us split the D°M’S’’ notation into parts:

= 45° + 30’ + 20’’

We can write the above expression as:

= 45° + 30. 1’ + 20.1’’

Now, as 1’ = 1/60° and 1’’ = 1/3600°, let us plug in their values in the above expression:

= 45° + 30. 1/60° + 20.1/3600°

= 45° + 0.5° + 0.0055°

= 45.5055°

Now that we have converted our D°M’S’’ notation into decimal notation, let us convert it into radians now:

= 45.5055°. (π/180)

= 0.2528π

Therefore, we have converted our D°M’S’’ notation into radians.

*All images/mathematical drawings were created with GeoGebra.*