Understand radian measure as arc length on the unit circle.
Interpret a directed radian rotation and its terminal point
Problem
Use the method diagram to analyze the directed unit-circle rotation \(θ~=~-\pi~/2\). State its direction, number of complete turns, remaining rotation, least nonnegative coterminal angle, and terminal point.
Analyze a directed angle in layers: its sign gives rotation direction, multiples of a full turn give the complete-turn count, and the remainder locates the terminal ray. Adding a full turn can replace a negative angle with a least nonnegative coterminal one without changing the endpoint. The axis or quadrant then determines the unit-circle coordinates.
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