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Unit Circle and Trigonometric Functions

Unit Circle and Trigonometric Functions
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2019-08-21 17:28
CircleVectorFunctionTrigonometryGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric functions (sine, cosine, tangent, etc.). It involves core mathematical concepts such as the unit circle, definitions of trigonometric functions, angle and radian conversion, and vectors. The construction uses GeoGebra commands like Intersect (intersection), Point (point), Circle (circle), Line (line), Rotate (rotation), Angle (angle), OrthogonalLine (perpendicular line), and Segment (segment). It is suitable for high school mathematics students to learn and understand the geometric meaning of trigonometric functions, as well as for university basic mathematics teaching.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → C
  4. Circle(A, 1) → c
  5. Point(yAxis) → E
  6. Point(yAxis) → F
  7. Line(E, F) → a
  8. Point(xAxis) → G
  9. Line(B, G) → b
  10. Rotate(B, θ, A) → B'
  11. Angle(B, A, B') → β
  12. Line(A, B') → h
  13. Intersect(c, h, 1) → D
  14. OrthogonalLine(D, b) → e
  15. OrthogonalLine(D, a) → f
  16. Intersect(b, e) → H
  17. Intersect(a, f) → I
  18. Segment(D, H) → sine
  19. Segment(I, D) → Cosine
  20. Intersect(c, a, 1) → J
  21. OrthogonalLine(J, a) → g
  22. Intersect(g, h) → K
  23. Intersect(c, b, 1) → L
  24. OrthogonalLine(L, b) → i
  25. Intersect(i, h) → M
  26. Segment(M, A) → Secant
  27. Segment(K, J) → Cotangent
  28. Intersect(h, i) → N
  29. Segment(N, L) → tangent
  30. Segment(A, H) → cosine
  31. Segment(A, D) → j
  32. Point(b) → O
  33. Point(b) → P
  34. Segment(O, P) → k
  35. Point(a) → Q
  36. Point(a) → R
  37. Segment(Q, R) → l
  38. Segment(A, K) → cosecant