Trigonometry: Radians and Degrees

How do we measure angle?

We measure distance with a ruler and use units like feet, meter, mile, and lightyear. We measure time using a clock and use units of seconds, days, or millennia, among others. With angle we could use a protractor and also use many units: the turn, gradians, degrees, or radians. Measuring angle feels less intuitive than distance and time because we don't do it nearly as much. But, saying there are 12 inches in a foot is entirely analogous to saying there are 57.2957795 degrees in one radian.

Why do we have different units for measuring angle? What are the most important units for angle? How are the different units related and how do we convert between them? All of these questions - and more - are answered in this video.

Vote for your favorite unit of angle! In the comments below let everyone know which unit you prefer to use and why. As I say in the video, I use radians about 99.9% of the time. But, I like the turn because it has a simple idea behind it. In terms of the arc length s of a portion of a circle with radius r, these two choices have the formulas:

s = rA (where A is the angle measured in radians)

s = CA (where A is the angle in turns and C is the circumference)

Notice that the arc length for an angle of one radian is the same as the radius - nice! The arc length corresponding to one turn is the circumference - also nice! What does the arc length formula look like in your favorite unit of angle?

Видео Trigonometry: Radians and Degrees канала New Planet School