Test
Trigonometry on the Unit Circle
This test explores angles of any magnitude and direction and their representation on the unit circle. Tasks cover coterminal-angle reduction, periodicity and the use of inverse trigonometric functions.
Time left: 00:00:00
Sample questions
- Calculate sin ___°.
- Simplify sin(−___°).
- Simplify sin(___° + 360° · ___).
- Simplify tan(___° + 180° · ___).
- Calculate arcsin(___).
Rotation-angle trigonometry
A rotation angle is measured from the positive x-axis: anticlockwise angles are positive and clockwise angles negative. On the unit circle, the point has coordinates (cos α, sin α), and periodicity permits replacement by a coterminal angle.
Quadrants and radians
Quadrants determine the signs of sine and cosine, while tangent is positive in quadrants I and III. Use 180° = π radians for conversion. A reference angle gives the magnitude of a trigonometric value, but its sign must still be selected from the quadrant.
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