Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Convert 150° to radians.
2. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Convert 7π/4 to degrees.
3. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find an angle coterminal with −π/3 in [0,2π).
4. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find sin(5π/6).
5. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find cos(7π/4).
6. {'id': 'u04-l06', 'number': 6, 'title': 'Tangent and Reciprocal Functions on the Circle', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
A wheel of radius 4 turns through 3π/2 radians. Find arc length.
7. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Convert 150° to radians.
8. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Convert 7π/4 to degrees.
9. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find an angle coterminal with −π/3 in [0,2π).
10. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find sin(5π/6).
11. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
Find cos(7π/4).
12. {'id': 'u04-l07', 'number': 7, 'title': 'Circular Motion and Periodic Position', 'family': 'unitcircle', 'week': 12, 'unit': 4, 'unit_title': 'Angles, Radians & the Unit Circle', 'essential': 'How does circular measure connect angles, coordinates, arc length, angular velocity, and exact trigonometric values?', 'project': 'Unit Circle Construction & Circular Motion Study'}
A wheel of radius 4 turns through 3π/2 radians. Find arc length.