Waching daily Jun 28 2018

When measuring angles, there are two primary systems that are used: degrees and radians.

Most people are more familiar with degrees than radians.

If you know that there are 360 degrees in a circle or that a right angle is 90 degrees,

then you already know about this system.

You would also have seen the system if you've ever used the compass for hiking.

Mathematically, degrees are an arbitrary unit of measure.

Its origins date back to ancient civilizations that tended to use numbers like twelve and

sixty in their number systems because those numbers have so many factors.

But there's nothing inherent to angles that would lead us to this choice.

Whenever you write down an angle in degrees you must always include the degree symbol

or state in words that you're giving a measurement in degrees.

Mathematicians use radians far more often than degrees because radians have a meaningful

geometric interpretation.

The word radian is related to the word radius, which gives us a hint about its meaning.

Suppose you have a circle of radius r.

If you pick a point on the circle and travel a distance r around the circumference of the

circle, the angle formed by your starting point, the center of the circle, and your

ending point is one radian.

In other words, it's the distance of one radius going around the circle.

It turns out that no matter the radius of your circle you will always get the same angle

When you do this.

The universality of this geometric property is among the many reasons mathematicians prefer

radians.

The formula for the circumference of a circle is C equals 2 pi r where pi is a mathematical

constant whose value is approximately 3.14159.

In other words, if we take one full trip around the circle we will travel a distance of two

pi radiuses.

This tells us that the angle measure of a whole circle is 2 pi radians.

In the next video, we will talk about some important angles and how to convert from degrees

to radians or the other way around.