I'd like to take Alan's explanation and expand upon it a little.
NOTE: THIS IS ONLY TRUE AS THE ANGLE TENDS TO 0
Thecircumferenceofacircleis$2πr$Iftheradiusis1unitthenthecircumferenceis$2π$Soiftheangleismeasuredinradiansthenthearclengthwillbeequaltotheanglethatitissubtendedfrom.Thisisforaunitcircle.
I'd like to take Alan's explanation and expand upon it a little.
NOTE: THIS IS ONLY TRUE AS THE ANGLE TENDS TO 0
Thecircumferenceofacircleis$2πr$Iftheradiusis1unitthenthecircumferenceis$2π$Soiftheangleismeasuredinradiansthenthearclengthwillbeequaltotheanglethatitissubtendedfrom.Thisisforaunitcircle.
Here's the proof of this using the "Squeeze Theorem".....it's somewhat complicated, but if you have some patience, I think you will appreciate the geometry involved. The proof is the first one on the page.
http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx
Thanks to Paul's Online Math Notes for this one.....(I certainly couldn't have derived it!!!)
BTW....."Paul" is Dr. Paul Dawkins...he's a professor at Lamar University in Texas