#### What is the deal with radians anyway?

Most of you are used to thinking of a circle in terms of degrees: 360° is the whole circle. 180° is half the circle etc... Well, radian measure is just a different way of talking about the circle. Radian measure is just different unit of measure.

Just as we can measure a football field in yards or feet--we can measure a circle in degrees (like the good old days) or in radians (welcome to the big leagues!)

Think about what the word *radian* sounds like...well, it sounds like 'radius', right? It turns out that a radian has a close relationship to the radius of a circle

#### So what is a radian then?

**Definition of radian: ** a radian is the measure of an angle that, when drawn a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle.

### Demonstration of Radian of Circle

The video below is an animation of 1 radian. Notice how the length of 1 radius stretches out to a portion of the circle. That portion is 1 radian of the circle.

There is a simple formula to convert radians to degrees. 1Π radian = 180. Therefore you can easily convert from one unit of measure to the other

### Degrees to radians

The general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180°

##### Example 1

Convert 200° into radian measure:

$ 200 ^{\circ} \cdot \frac{\pi }{ 180 ^{\circ}} \\ = \frac{10\pi}{ 9} \text{ radians } = \text{3.49 radians } $

##### Example 2

Convert 120° into radian measure:

$ 120 ^{\circ} \cdot \frac{\pi }{ 180} = \frac{2\pi}{ 3}\text{ radians }= \text{2.09 radians } $