Robust Posted April 21, 2005 Report Share Posted April 21, 2005 One of the more frequently asked questions I get from graduate and undergraduate students alike is how to determine the distance between each angular degree on circumference of the circle. For those here who might ask, the answer is quite straightforward: radius/radian. Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 21, 2005 Report Share Posted April 21, 2005 One of the more frequently asked questions I get from graduate and undergraduate students alike is how to determine the distance between each angular degree on circumference of the circle. For those here who might ask, the answer is quite straightforward: radius/radian.So let's make sure I understand you here. To make things easy let's use a unit circle so the radius=1. Now the distance halfway around the circle is pi radians so you're saying the distance between 0° and 180° on the circumference is 1/pi? The distance all the way around the circle is 1/2pi? One degree is pi/180 radians right? So the distance along one degree is 1/(pi/180)? Is this what you're saying? :) Quote Link to comment Share on other sites More sharing options...
Robust Posted April 21, 2005 Author Report Share Posted April 21, 2005 So let's make sure I understand you here. To make things easy let's use a unit circle so the radius=1. Now the distance halfway around the circle is pi radians so you're saying the distance between 0° and 180° on the circumference is 1/pi? The distance all the way around the circle is 1/2pi? One degree is pi/180 radians right? So the distance along one degree is 1/(pi/180)? Is this what you're saying? :)No, Clay. What I'm saying is exactly as stated: radius/radian = degree-distance. You give a radius of 1.0, so with a radian of 57.2957....then tthe distance between each angular degree on the circumference would be: 1/radian = 0.01745.... unit. Quote Link to comment Share on other sites More sharing options...
Bo Posted April 21, 2005 Report Share Posted April 21, 2005 i always though radians where between 0 and 2pi... anyways, the definition is clear :)distance on circle/angle = radius/angle Bo Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted April 21, 2005 Report Share Posted April 21, 2005 Perhaps it's clearer to say: angle = arc/radius where angle will be given in radians, the ratio of two lengths. Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 21, 2005 Report Share Posted April 21, 2005 i always though radians where between 0 and 2pi...They are. Robust is busy inventing new math again.... Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted April 22, 2005 Report Share Posted April 22, 2005 Robust is busy inventing new math again....A noble activity, providing it's done properly. Quote Link to comment Share on other sites More sharing options...
Robust Posted April 23, 2005 Author Report Share Posted April 23, 2005 They are. Robust is busy inventing new math again.... There's no new maths here at all, people. The radian is simply that distance on the arc as that of the radius which subtends it. Accordingly then, radius/radian gives the distance between each angular degree on the circumference.....as clearly shown by the given example.. I have given you new maths, but this certainly ain't it! Quote Link to comment Share on other sites More sharing options...
Rincewind Posted April 23, 2005 Report Share Posted April 23, 2005 No, Clay. What I'm saying is exactly as stated: radius/radian = degree-distance. You give a radius of 1.0, so with a radian of 57.2957...The radian is simply that distance on the arc as that of the radius which subtends it. Accordingly then, radius/radian gives the distance between each angular degree on the circumference...If the radian is the distance on the arc equal to the radius, then if the radius = 1, then the radian = 1, and radius/radian = 1, not 0.01745. Quote Link to comment Share on other sites More sharing options...
Robust Posted April 23, 2005 Author Report Share Posted April 23, 2005 If the radian is the distance on the arc equal to the radius, then if the radius = 1, then the radian = 1, and radius/radian = 1, not 0.01745. No, Rincewind, the radian = 360-degrees/2pi. It is not determined by linear length (as is the radius). Quote Link to comment Share on other sites More sharing options...
tom Posted April 23, 2005 Report Share Posted April 23, 2005 We all now that the length of an arc is L = angle ( in radians ) * radius angle ( in radians) = angle ( in degrees ) / 360 * 2 pi L = angle ( in degrees ) / 360 * 2 pi * radius We're talking about 1 degree so L = 1 / 360 * 2 pi * radius L = 2 pi / 360 * radius 360 / 2pi is the angle in degrees corresponding to an angle of 1 radian . To call this radian is not correct. He says something true ;) , but in his unique way Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 23, 2005 Report Share Posted April 23, 2005 There's no new maths here at all, people. The radian is simply that distance on the arc as that of the radius which subtends it. Accordingly then, radius/radian gives the distance between each angular degree on the circumference.....as clearly shown by the given example.. I have given you new maths, but this certainly ain't it!Plenty of new math. A circle is 2π radians and the circumference of that circle is radius*2π not the radius/2π. Quote Link to comment Share on other sites More sharing options...
Damo2600 Posted April 24, 2005 Report Share Posted April 24, 2005 Perhaps it's clearer to say: angle = arc/radius where angle will be given in radians, the ratio of two lengths. Even better: arc = angle/radians Quote Link to comment Share on other sites More sharing options...
Damo2600 Posted April 24, 2005 Report Share Posted April 24, 2005 Sorry that's wrong: arc = radians / angle IF angle is given as a fraction of 180 degrees. degree distance = (pi)r / 180 Stuff it: radius / radians is much better. Quote Link to comment Share on other sites More sharing options...
Robust Posted April 25, 2005 Author Report Share Posted April 25, 2005 Plenty of new math. A circle is 2π radians and the circumference of that circle is radius*2π not the radius/2π. You protest too quickly, Clay. The post does not relate to determining circumference but to the distance between each angular degree on the circumference - most readily given as radius/radian. Have you tried it? Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 25, 2005 Report Share Posted April 25, 2005 You protest too quickly, Clay. The post does not relate to determining circumference but to the distance between each angular degree on the circumference - most readily given as radius/radian. Have you tried it?Be it one degree or 360 of them, the distance is still the radius times the angle in radians, not the radius divided by the angle in radians. Quote Link to comment Share on other sites More sharing options...
Robust Posted April 25, 2005 Author Report Share Posted April 25, 2005 Be it one degree or 360 of them, the distance is still the radius times the angle in radians, not the radius divided by the angle in radians. You got it just backwards, Clay. The distance between each angular degree on the circumference is given by radius/radian (as the quickest result). Quote Link to comment Share on other sites More sharing options...
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