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Basic Trig Functions on the Unit Circle

Basic Trig Functions on the Unit Circle
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2015-12-30 11:42
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between any point on the unit circle and its corresponding trigonometric values. Key math concepts include the unit circle, trigonometric definitions, ratios, and vectors. GeoGebra commands and objects used in construction are Sequence, Point, Angle, Circle, Segment, and Midpoint. It is suitable for high school mathematics education, helping students understand the intrinsic connection between trigonometric functions and the unit circle, laying a foundation for advanced topics in analytical geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[(r, 0), k°, (0, 0)], k, 0, 360) → list1
  2. Point(list1) → P
  3. Angle((1, 0), (0, 0), P) → θ
  4. Circle((0, -0.004807882852143508), r) → c
  5. Segment((0, 0), P) → a
  6. Segment((0, 0), (x(P), 0)) → b
  7. Segment(P, (x(P), 0)) → d
  8. Midpoint(b) → A
  9. Midpoint(d) → B
  10. Midpoint(a) → C
  11. Segment(E, E - (0, 0.025)) → i
  12. Segment(F, F - (0, 0.025)) → j
  13. Segment(G, G + (0.025, 0)) → k
  14. Segment(H, H + (0.025, 0)) → l
  15. Angle(P, (x(P), 0), (0, 0)) → α
  16. Sequence(Rotate[(r, 0), k°, (0, 0)], k, 0, 360) → list1_1
  17. Point(list1_1) → P_1