Talk:Radian/Dimensional analysis

I propose adding the following to the article. I'd put it in there myself, but I'm not sure what phrasing will work out the best, or whether I'll be able to finish the links and equations in this session. Also, note that according to SI supplementary unit, the radian is now considered to be an SI derived unit.

Formally, the radian isn't a unit; anything measured in radians is dimensionless. This can be seen easily in that the ratio of an arc's length to its radius is the angle of the arc, measured in radians. The quotient of two distances is dimensionless.

Another way to see the dimensionlessness of the radian is in the Taylor series for the trigonometric function $$\sin(x)$$:
 * $$\sin(x) = x - \frac{x^3}{3!} + ...$$

If $$x$$ had units, then the sum would be meaningless; the linear term $$x$$ can not be added to the cubic term $$x^3/3!$$, etc. Therefore, $$x$$ must be dimensionless. --Snags 01:28, 12 Feb 2004 (UTC)


 * Looks good.--Patrick 22:56, 12 Feb 2004 (UTC)


 * I have added it with minor tweaks. --Doradus 21:40, Sep 18, 2004 (UTC)