Radians and DegreesDate: Mon, 21 Nov 1994 15:31:39 -0900 From: Patryce McKinney Why are radians preferable to degree measures? Patryce wvhppdm@northstar.k12.ak.us Fairbanks, Alaska Date: Mon, 21 Nov 1994 20:00:54 +0000 From: Elizabeth Weber Hi Patryce! The only reason I know of that radians are often preferable to degree measures is that when you're expressing things in radians, they LOOK more like fractions of a circle. If you see a number like 3p/2 radians, it looks a lot more like 3/4 of a circle (which it is) than a number like 270 degrees, even though 270 degrees means exactly the same thing. Perhaps some of the other math doctors know other reasons--if they do, you'll hear from them too! Thanks for writing to Dr. Math, Elizabeth, a math doctor Date: 30 Nov 1994 16:38:34 GMT From: Math Doctor Organization: Swarthmore College Hello there Patryce! Here's the main reason I know of that people like radians better than degrees. Do you know how to find out the arc length of part of a circle? You take the fraction (like 1/3, or 3/7 or something) of the circle that that arc is, and you multiply that by the total circumference of the circle. Well, as it turns out, when you use degrees, you have to have some nasty conversion factor in there to figure out the fraction of the circle that the arc is, but when you use radians, you just multiply (the angle subtended by the arc, measured in radians) times (the radius of the circle). A nice formula. Try to derive the formula for the length of an arc of a circle, given the degree measure of the angle that subtends it. Is it a nice formula? The way things work out, the formula for arc length is used to derive a whole bunch of other things. So it makes sense to use the units that will make everything come out nicely. If you have any more questions, be sure to write back! -Ken "Dr." Math |
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