Radians (Radius Invariance Property)
This figures illusrates how the ratio of arc-length over ratio for the angle doesn’t change for two radius choices. This radius invariant property is one of the reason that radians are the preferred system for measuring angle This is discussed on the concept page for radians and in the page which discusses radians vs. degrees.
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Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.
This page compares and contrasts the two systems of measuring angles in math: radians and degrees, and explains why radians is the preferred unit of measure for angles.