Turns are better than radians
&gt; <i>But math never decreed that sine and cosine have to take radian arguments!</i><p>That is not entirely true. It comes from the relationship between those functions and the complex numbers via the Euler formula.<p><pre><code>     ix
    e    = cos x   +   i sin x
</code></pre>
There may be arithmetic&#x2F;numerical inconveniences, but that&#x27;s not all there is to &quot;math&quot;.<p>Let&#x27;s define ncos and nsin (&quot;nice cos, nice sin&quot;) as follows:<p><pre><code>   nsin x = sin 2πx
   ncos x = cos 2πx
</code></pre>
So then what do we make of:<p><pre><code>   ncos x   +   i nsin x
</code></pre>
This has to be<p><pre><code>   cos 2πx  +   i sin 2πx
</code></pre>
which is then<p><pre><code>     2πix        (   2π) ix        ix 
   e           = ( e   )      =  f 

      
           2π</code></pre>
Where f = e    is a weird number like 535.4916. This f doesn&#x27;t have nice properties. E.g.:<p><pre><code>      d     x           x
      -   f     &#x2F;=    f 
      dx
</code></pre>
Otherwise it works; for instance 90 degrees is 0.25 and surely enough<p><pre><code>     0.25i 
   f          = i
</code></pre>
In situations not involving e in relation to angular representations via Euler, f cannot replace e.<p>I&#x27;m all for having parallel trig functions in libraries that work with turns, though.<p>The annoying 2π factor shows up in lots of places though. Should way, say, in electronics, redefine a new version of capacitive reactance which doesn&#x27;t have 2πf in the denominator, but only f?