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Visual Proof of Sine and Cosine Angle Sum Formulas

Visual Proof of Sine and Cosine Angle Sum Formulas
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2016-01-28 23:54
AngleFunctionTrigonometryGeometric ConstructionGraphing
In collections Fun with Functions
This example demonstrates the sine and cosine angle sum formulas through a visual construction. It involves core math concepts like trigonometric functions, angles, and geometric proofs. The construction uses GeoGebra commands such as Angle, Polygon, RotateText, VerticalText to illustrate the derivation process, making it suitable for high school students and math enthusiasts learning about trigonometric properties and geometric proofs.

GeoGebra Commands & Parameters

  1. Angle(A, O, B) → γ
  2. Angle(B, A, O) → θ
  3. Polygon(O, A, B) → poly1, b, o, a
  4. Angle(B, O, D) → δ
  5. Angle(D, B, O) → η
  6. Polygon(O, B, D) → poly2, d, o_1, b_1
  7. RotateText("1", sum) → text14
  8. RotateText("cos β", α) → text1
  9. RotateText("sin β", α - 90°) → text5
  10. VerticalText("sin α cos β") → text7
  11. Polygon(B, C, D) → poly3, d_1, b_2, c
  12. Angle(C, B, D) → ζ
  13. VerticalText("cos α sin β") → text3
  14. Polygon(O, D, E) → poly4, e, o_2, d_2
  15. Angle(E, D, O) → ε
  16. VerticalText("\sin(α+β)") → text4