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Trigonometric Ratios on the Unit Circle

Trigonometric Ratios on the Unit Circle
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2018-03-02 18:52
CircleTrigonometryGeometric Construction
This example demonstrates trigonometric ratios (SOHCAHTOA) on the unit circle. By constructing angles and their corresponding trigonometric values on the unit circle, it helps students understand the concepts of sine, cosine, and tangent. It uses GeoGebra commands such as Sequence, Point, Angle, Circle, Segment, and Midpoint. Suitable for students in middle school and above learning 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