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Cosine Difference Formula Proof

Cosine Difference Formula Proof
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2019-10-22 21:23
FunctionTrigonometryGeometric Construction
This example dynamically demonstrates the proof of the cosine difference formula. It involves core mathematical concepts such as trigonometric functions, geometric construction, and symmetry. The construction uses GeoGebra commands like Circle, Point, Segment, CircleArc, and Angle. Suitable for high school mathematics students and learners seeking a deeper understanding of trigonometric identities.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. Segment(D, A) → h
  5. CircleArc(A, B, D) → d
  6. Point(d) → C
  7. Segment(A, C) → g
  8. Angle(D, A, B) → β
  9. Angle(D, A, C) → α
  10. Angle(B, A, C) → γ
  11. Segment(C, B) → i

AI Drawing Prompt Reference

Draw a unit circle centered at point A and mark point B on the circle. Connect point A to B, and then connect point D to A. Draw an arc with A as the center and B and D as endpoints, intersecting the circle at point C. Connect point A to C to form angles β and α, and connect point C to B to form angle γ.
The prompt above was compiled from the original drawing commands and is for reference only.