Understanding Radian Measure

A circle O with radius 1 unit has its center placed at the origin. Let A be its intersection with the x-axis at (1,0) and P be another point on its circumference. If we move P along its circumference, then we can determine the distance traveled by P. If we let A be the starting point of P as it moves counterclockwise, then the distance traveled by P is equal to the length of arc AP represented by the red arc in the following figure.

radian 2

To be able to know the length of arc AP, first, we must know the total distance traveled by P from A going counterclockwise and back to A  (i.e. complete revolution). That is, we need to find the circumference of the circle. Since a unit circle has radius 1 unit, its circumference C is  » Read more