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Test: Rotation-angle trigonometry

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.

Question qty: 10
Duration in minutes: 10
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Sample questions

  • Simplify sin(−a°).
  • Calculate sin a°.
  • What are the signs of sine and cosine in quadrant III?
  • Simplify sin(a° + 360° · k).
  • Calculate arcsin(s).
  • Simplify tan(a° + 180° · k).
  • Which statement about trigonometric periods is correct?
  • Calculate arccos(s).

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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