Now that you’ve become an expert at converting units and rates, we can now extend our understanding of this concept to convert units used to measure **angles** in trigonometry, namely **degrees** and **radians**. An **angle** is a geometric figure consisting of two rays with a common endpoint. The angle below is represented by the universal symbol for angles – the Greek letter theta (θ) – and it’s formed by joining the two line segments.

The **degree** (°) is a unit of angular measure equal to 1/360 of a **revolution**; thus, 360º = 1 revolution. A degree can be further split into minutes and seconds:

- 1 minute (‘) is equal to 1/60 of a degree.
- 1 second (”) is equal to 1/3600 of a degree.
- These will serve as the main conversion ratios used in this lesson.

Some examples of angles written in **degrees, minutes, and seconds** (DMS):

**85° 18′ 42″**(85 degrees, 18 minutes, 42 seconds)**62° 12′**(62 degrees, 12 minutes)- Note that minutes or seconds less than 10 are written with an initial zero.

**75° 06′ 03”**(75 degrees, 6 minutes, 3 seconds)

Let’s learn how to convert between decimal degrees (i.e. 33°) to DMS and *vice versa*. The first example shows how to convert DMS to **decimal degrees**, while the next demonstrates the reverse process.

Now the reverse. As a challenge, try converting on your own before starting.

If you took the calculator recommendation seriously before enrolling into this course, the **Casio fx-991ES Plus **calculator was suggested due to its large volume of pre-programmed functions, one of which is this precise conversion. The last video outlines the steps to doing this. If you have a similar calculator, try locating these buttons – you might be lucky enough to have it!