Turns are better than radians
&gt;But math never decreed that sine and cosine have to take radian arguments!<p>Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler&#x27;s formula (e^ix = cosx + isinx) is the simplest when working with radians.<p>Of course you can work in other units, but you&#x27;ll need to insert the appropriate scaling factors all over the place.<p>&quot;Turns&quot; don&#x27;t generalize to higher dimensions either. With radians you can calculate arc length on a circle by multiplying with the radius. This extends naturally to higher dimensions: a solid angle measured in steradians lets you calculate surface area on a sphere by multiplying with the radius. How do you do the same with &quot;turns&quot; on a sphere? You can&#x27;t in any meaningful way.