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Pc 4.1 Angles and Their measures

Angles and their measures

Angles and their Measures

Angle measure in radians and with arc length

Most of us understand angles from Geometry.  However we only discussed angle measure in degree form. In this section we will explore angles and their measures in Radians and Degree-Minutes-Seconds or DMS form.  These are equivalent ways to measure angles and we will use all three in later chapters so it is important to understand them now as well as how to convert from one to another.

In these first two videos we will introduce you to degrees, minutes and seconds. While it is nice to have answers in whole degrees, often we will deal with angles in smaller portions of a degree. To express the measure of a portion of a degree we can either use decimals or minutes and seconds. I will introduce as well as show you how to convert between the two.

How to convert and angle from degrees to DMS

How to convert an angle from DMS to Degrees

The measure of an angle in degree form is often preferred because it is what most students are used to. However the definition of a radian actually has some meaning behind it where it came from. The history of the reasoning behind the measure of a degree is disputed where as the measure of a radian is pretty straightforward. I explain it here.

What is a radian?

How to convert an angle from Degrees to Radians

How to convert an angle in Radians to Degrees


Lastly we will begin our investigation of arc length. If we are given

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