Why 6.28 Radians?Date: 10/07/98 at 21:16:44 From: Jason Subject: Radians Why is a circle divided into approximately 6.28 radians? Date: 10/08/98 at 13:18:41 From: Doctor Peterson Subject: Re: Radians Hi, Jason, A complete circle, 360 degrees, is exactly 2 pi radians. Do you recognize that from the formula for the circumference of a circle, 2 pi r? That's because the number of radians in an angle is defined as the length of the arc of a unit circle subtended by the angle: *********** ****** ****/* *** / *** *** / *** * / * L ** / ** * / * * / * * / * * / * * / A * * *------------------------ * 1 * * * * * * * * * ** ** * * *** *** *** *** ****** ****** *********** The radian measure of the angle A is defined as the length of the arc L. You can think of radians as just using a flexible tape measure to measure around the circle - the most natural way to measure an angle. So if A is the whole circle, its measure is the whole circumference, or 2 times pi, which is about 6.28. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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