Circle Sector AreaDate: 03/20/2003 at 21:40:05 From: Trevor Subject: Mandatory conversion Is it mandatory to convert degrees to radians when finding the area of a sector of a circle? Example: Find the area of a sector of a circle of radius 4 that is intercepted by a 150-degree central angle. It doesn't say it has to be in radians. A = (1/2) r^2 theta .5*16*150 = 1200 units or .5*16*(150 Pi/180)= 20Pi/3 Date: 03/20/2003 at 23:02:51 From: Doctor Peterson Subject: Re: Mandatory conversion Hi, Trevor. There is a formula for sector area in terms of degree measure, but it is essentially a conversion to radians - in fact, that's what your last line looks like. If you use the formula that takes radians, then you have to use radians. Here is the degree-based formula. Since the area of a sector is proportional to its central angle, and the area of a whole circle is pi r^2, the area of a sector with central angle T degrees (out of 360 for the whole circle) is A = pi r^2 * T/360 = pi/360 r^2 T If T is in radians, then the formula is A = pi r^2 * T/(2 pi) = 1/2 r^2 T The same is true of the arc length formula. In degrees, s = 2 pi r * T/360 = pi/180 r T and in radians, it is s = 2 pi r * T/(2 pi) = r T The latter is the main reason for using radians at all. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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