Although we know how many degrees a right triangle’s right angle is, we don’t really get to know radians until geometry and trigonometry comes around near high school. There are 360 degrees in a full turn, but in radians, 2π is equal to a full turn. Is there a reason for these numbers? Let’s find out.
Radians is very easy to explain. We know by at most fifth grade math that the formula for finding the circumference of a circle via the radius is 2πr. I believe that 2π was used as a full turn because 2π is the circumference of a circle when the radius is 1 unit. This is reasonable because when you go half a circle it is π in radians in circumference when r=1.
Degrees is more difficult to explain. I did some research and, turns out, it’s the Sumerians and the Babylonian’s fault that we have 360 degrees, a strange number; it would be easier to have a number like 1000 or 100, right? The reason why is that the Sumerians realized the pattern that a year is close to 360 days, so the Sumerians thought that they rotated around 1 degree per day. This also made it easier to count with the Babylonian base-60 system, and it stuck to today.
Degrees and radians are both very effective ways to measure the degrees of any angle. I believe that any kind can perform well in any math problem. Maybe one way is more effective than the other, but they all have the same purpose: to measure degrees on an angle.