A radian is the distance around the circle that the radius and angle make. π is half of a circle and 2π is the whole 360 degrees. Radians and the unit circle relate because the points on the unit circle can be figured out by and then measured in radians. The main points on the unit circle are found by using sin and cos and can be converted into radians. Also, the main points on the unit circle are measured and used in radians. Radians relate to circumference because the formula for circumference is C=2πr and r is radius. The radius is used to measure a radian. Radians relate to degrees because each radian degree can be converted into degrees to be measured differently. For an example, the convert radians to degrees, you times is by 180/π and if you wan to convert from degrees to radians, you times it by π/180. I prefer radians because it is usually how things are measured in formulas and it is easier to just use radians instead of converting to degrees and then back to radians. I like either way, I just think radians is easy and faster. Radians also seems more mathematically pure because the formulas were made for that unit and also things could be confused while converting.
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