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Why is it 1
It was freely chosen for simplicity.
If you choose another R, the other sides (x and y) become R*cos(th) and R*sin(th)
I don't understand what is harmful about the unity circle either.
Any circle could have its radius technically be 1, as long as you set the units of measurement so that 1 equals the radius of the circle.
units? what are those? I never use units, or pay attention to capitals. pure math ftw, baby!
spoiler
Rapidly hides from the science professors
Pure math uses units. Like they say "1 unit"
Sometimes the units are given cute names like "wiggly waggly units" to make physicists cringe. Acknowledging a unit with cute names when the unit is not important is entertaining.
Because it's a unit circle.
for the same reason that rulers start with 1, it would be utterly pointless to use anything else.
Your ruler starts with 1? How do you measure stuff between 0 and 1?
those are unlabeled, have you ever seen a ruler?
I am fascinated, can you show a picture
Zero is not unlabelled lol