Arc FormulasDate: 05/08/2003 at 12:03:04 From: Rick Subject: Remembering formula to use I am trying to determine the angle of an arc from the radius and arc length. The radius is 630 and the arc length is 66.82. How can I remember the formula? Date: 05/08/2003 at 14:37:31 From: Doctor Ian Subject: Re: Remembering formula to use Hi Rick, Here's how I remember it. If you have a circle with radius 1, the circumference of the circle will be 2*pi, which is also the number of radians in the circle. If I double the radius of the circle, I double the circumference, but the number of radians stays the same. If I triple the radius, I triple the circumference, and so on. In general, if the radius of the circle is R, then the circumference is 2*pi*R, but the number of radians stays the same. So (radius of circle) * (angle in radians) = (arc length) which is usually abbreviated R * theta = s In your case, you know R and s, and you want to find theta, so you can rearrange it to get theta = s/R Note that the result will be in radians, not degrees. To convert, you just have to remember that 2*pi radians (i.e., once around the circle) is the same as 360 degrees (also once around the circle). So to convert to radians, you can multiply by this scale factor: 360 degrees ___ radians * ----------- = ___ degrees pi radians If that's too complicated, here's another way to think about it. Suppose you have a circle with radius 660 cm. The circumference of the circle will be circumference = 2 * 660 * pi right? So that corresponds to 360 degrees. And you have some part of that arc length, so you can set up and solve a proportion: ? degrees 66.82 cm ----------- = ----------------- 360 degrees (2 * 660 * pi) cm Consider some test cases to see why this works. If your arc is the same as the circumference, you should end up with 360 degrees, and you do. If your arc is half the circumference, you should end up with 180 degrees, and you do. Basically, the ratio of the arc length to the circumference is the same as the ratio of the angle to the whole 360 degrees of the circle. Does that make sense? If you're not sure how to solve the proportion, take a look at Flipping and Switching Fractions http://mathforum.org/library/drmath/view/58193.html Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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