On 2010-10-12 11:16:09 +0100, Ben said:
Angles aren't "true" units, as they are ratios of two lengths. They are more of a "pseudo" unit.
That's right, in fact angles are pure numbers. In general any function which raises its argument to more than one power (for instance anything with a non-trivial power series (Taylor series) expansion) doesn't make much sense if its argument has units. Transcendendal functions are all like that, of course.
For instance sin(x) = x + s^3/6 + O(x^5), so sin(1m) would be 1m + 1m^3/6 + O(m^5), and it doesn't make sense to add metres and cubic metres (let alone the infinite number of higher-order terms!).
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