Primarygun Posted November 14, 2004 Share Posted November 14, 2004 How does radian bring convenience to us? Could anyone tell me? Link to comment Share on other sites More sharing options...
psi20 Posted November 14, 2004 Share Posted November 14, 2004 Radians in trigonometry are used in trignometric graphs, sectors, angular speed, arc lengths, polar graphs, etc. They might also be a mnemonic thing. In the unit circle, the angles with a denominator of 4 have sqrt 2 / 2 (2*2 = 4)as their coordinates and you have to think which quadrant they're in. denominators of 6 have sqrt 3 / 2 as x-coordinate (3*2 = 6) . denominators of 3 have 1/2 as x-coordinate (1+2=3?). That may/may not be a convienience. I'm not good with mnemonics, though, so that doesn't apply to me. Link to comment Share on other sites More sharing options...
matt grime Posted November 14, 2004 Share Posted November 14, 2004 The convenience is that if the argument is in radians then differentiating sin gives cos, etc. If it were degrees then the derivative of sin would be something like (2pi/360)cos Link to comment Share on other sites More sharing options...
Primarygun Posted November 15, 2004 Author Share Posted November 15, 2004 Is it useless? Link to comment Share on other sites More sharing options...
matt grime Posted November 15, 2004 Share Posted November 15, 2004 Of course it's not useless (no more so than any other unit). It is analytically (ie in terms of calculus) and geometrically the correct measure of angle. It simply and directly relates angle to arc length and sector area. Degrees are the convenient one - their sole benefit is to divide the circle in to units such that 2,3,4,5,6,8,9,10,12 divide the whole - it serves no other use than this numerical one. Link to comment Share on other sites More sharing options...
Sayonara Posted November 15, 2004 Share Posted November 15, 2004 Haven't we done this before? Link to comment Share on other sites More sharing options...
123rock Posted November 17, 2004 Share Posted November 17, 2004 Radians aren't units Link to comment Share on other sites More sharing options...
123rock Posted November 17, 2004 Share Posted November 17, 2004 Radians aren't units Link to comment Share on other sites More sharing options...
Primarygun Posted November 17, 2004 Author Share Posted November 17, 2004 Is degree a unit? Link to comment Share on other sites More sharing options...
Primarygun Posted November 17, 2004 Author Share Posted November 17, 2004 Is degree a unit? Link to comment Share on other sites More sharing options...
swansont Posted November 17, 2004 Share Posted November 17, 2004 Is degree a unit? No. I think of degrees and radians as pseudounits - you need to keep track of them to be consistent, but they are an implied ratio (fractions of a circle) and as such don't really have any dimension. Link to comment Share on other sites More sharing options...
swansont Posted November 17, 2004 Share Posted November 17, 2004 Is degree a unit? No. I think of degrees and radians as pseudounits - you need to keep track of them to be consistent, but they are an implied ratio (fractions of a circle) and as such don't really have any dimension. Link to comment Share on other sites More sharing options...
123rock Posted November 20, 2004 Share Posted November 20, 2004 Since a degree is measured by the length of the arc divided by the radius of a circle, they aren't unites, since it's distance/distance. Link to comment Share on other sites More sharing options...
123rock Posted November 20, 2004 Share Posted November 20, 2004 Since a degree is measured by the length of the arc divided by the radius of a circle, they aren't unites, since it's distance/distance. Link to comment Share on other sites More sharing options...
NSX Posted November 20, 2004 Share Posted November 20, 2004 I think the idea of radians is useful, because it relates the arc length, radius, and the angle subtended. In addition (like Matt said), it's useful in Calculus because degrees don't work there. In addition, steradians use the same idea as radians, whereas relating steradians to degrees would be different. Link to comment Share on other sites More sharing options...
NSX Posted November 20, 2004 Share Posted November 20, 2004 I think the idea of radians is useful, because it relates the arc length, radius, and the angle subtended. In addition (like Matt said), it's useful in Calculus because degrees don't work there. In addition, steradians use the same idea as radians, whereas relating steradians to degrees would be different. Link to comment Share on other sites More sharing options...
CPL.Luke Posted December 24, 2004 Share Posted December 24, 2004 why don't degrees work in calculus? Link to comment Share on other sites More sharing options...
Dave Posted December 25, 2004 Share Posted December 25, 2004 It's not that they won't work, rather that the answer you get is rather ugly. When you differentiate/integrate a trigonometric function, the answer turns out to be nice because we assume the angle is being measured in radians - e.g. sin differentiates to cos. If we were to use degrees when differentiating, we'd have 180s and pi's floating about everywhere. Link to comment Share on other sites More sharing options...
CPL.Luke Posted December 25, 2004 Share Posted December 25, 2004 yeah thats what I thought, i was starting to think I was doing something seriously wrong in my calc Link to comment Share on other sites More sharing options...
123rock Posted December 25, 2004 Share Posted December 25, 2004 I think that the reason there is a great deal of use for the radian is because since the unit circle has a radius of 1 (for ratio purposes), the circumference is 2pi and thus 2pi radians for both the degree measure and the length of the circumference. I realize that this is a false derivation of the use of radians, since even if you double the radius of the circle, you double the length of the circumference, but the degree measure is still 360 thus 2pi, since all circles are similar. That's why 180deg.=pi radians, and then they eventually got that 1 radian=about 52degrees. Link to comment Share on other sites More sharing options...
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