A radian is an angle measure based on the radius of a circle. Radians are written on terms of pi. For example on the unit circle pi is equal to half of the circle also called 180 degrees. A whole circle is 2pi radians. Radians relate to the circumfrene cause the arc length which is part of the circumfrence is measured in radians. Radians relate to degrees because they are both an angle measurement and if you know the angle measure in degrees you can find the radian measure and vice versa. For example 2 pi is 360 degrees. if you’re not referring to a unit circle and want to covert radians into degrees you multiply 2pi times 180/pi and the pi’s would cancel out leaving you with 360 degrees. I prefer degrees because when finding measures on a circle to the nearest reference angle, if the original angle is given in radians I have to convert it to degrees and then do the subtraction . However when working with degrees I don’t have to convert it. Although I prefer degrees I think radians are more mathematically pure because radians are exact and degrees sometimes have to be rounded.
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February 2017
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