Understand radian measure as arc length on the unit circle.
Convert radians to arc length, turns, and degrees
Problem
A circle has radius \(5~\text{units}\) and central rotation \(θ~=~2~\text{radians}\). Use the diagram to calculate the arc length, rotation in turns, and degree measure, including the requested exact and approximate forms.
The same rotation can be described three ways: multiply radius by radians for arc length, divide radians by a full turn for revolutions, and use the half-turn equivalence for degrees. Keep exact forms until the end, then approximate only when requested. The turn fraction should agree with the degree measure as a fraction of a full rotation.
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