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Sine 18 Construction

Sine 18 Construction
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2017-10-11 21:27
AngleTrigonometryGeometric Construction
This example demonstrates the geometric construction of an angle with a sine value of 18°. It involves core math concepts like trigonometry, geometric construction, angle measurement, and circle properties. Key GeoGebra commands and objects used include Point, Circle, Rotate, Segment, Intersect, AngularBisector, Angle, Distance, Midpoint, and LaTeX. Suitable for high school students learning the geometric meaning and construction of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point({0, 0}) → A
  2. Circle(A, 1) → c
  3. Point({1, 0}) → B_1
  4. Rotate(B_1, 18°, A) → C
  5. Rotate(B_1, (-(18°)), A) → D
  6. Segment(A, D) → f
  7. Segment(D, C) → g
  8. Segment(C, A) → h
  9. Intersect(i, g) → B
  10. AngularBisector(f, g) → j, k
  11. Intersect(k, h) → E
  12. Segment(E, D) → l
  13. Segment(A, B) → m
  14. Angle(C, B, A) → α
  15. Angle(A, B, D) → β
  16. Angle(C, D, E) → γ
  17. Angle(E, D, A) → δ
  18. Angle(B, A, C) → ε
  19. Distance(C, D) → distanceCD
  20. Midpoint(C, D) →
  21. Distance(C, B) → distanceCB
  22. Midpoint(C, B) →
  23. LaTeX(distanceCB, true, true) → text1
  24. LaTeX(distanceCD, true, true) → text2