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Trig Ratios on Unit Circle by Sam Waterfield

Trig Ratios on Unit Circle by Sam Waterfield
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2018-02-08 05:06
CircleAngleTrigonometryCoordinate Geometry
This example demonstrates the geometric meaning of trigonometric ratios (sine, cosine, tangent) for any angle on the unit circle. Key math concepts include the unit circle, definition of trigonometric functions, and angle-radius conversion. Construction highlights involve commands like Sequence, Point, Angle, Circle, Segment, Midpoint in GeoGebra, where a moving point P on the unit circle dynamically shows corresponding trig ratios. Suitable for high school students learning trigonometric definitions, and for teaching parametric equations and analytical geometry.

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