I was sitting the other day with my cousin, helping him with his homework, when he asked me what's the deal with these radians.

So I took a paper and a pen and tried to recall where did these radians come from, but something is not quite clear for me.

Consider the following circle:

When the angle is 90 degrees, arc

**a** is exactly

the length of the full circle's perimeter.

and therfor the angle in radians is:

So when r=1, we're good, we get:

But obviously, it is not the case for any other r, as it should be...

So what am I missing here?