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Six Trigonometric Function Values as Vector Lengths

Six Trigonometric Function Values as Vector Lengths
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2016-07-11 06:47
VectorTrigonometryCoordinate GeometryGeometric Construction
This example visually demonstrates the values of six trigonometric functions through vector lengths. It involves core concepts like vectors, trigonometric functions, and coordinate systems. Key GeoGebra commands/objects used in construction include Intersect, Circle, Line, Point, Angle, Vector, and Segment. Suitable for high school mathematics education to help students understand the relationship between trigonometric functions and vector lengths, enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Intersect(c, yAxis, 2) → C
  5. Line(B, yAxis) → TangentAxis
  6. Line(C, xAxis) → CotangentAxis
  7. Point(c) → D
  8. Line(A, D) → Secant
  9. Intersect(CotangentAxis, Secant) → E
  10. Intersect(c, Secant, 1) → F
  11. Intersect(TangentAxis, Secant) → G
  12. Angle(B, A, D) → α
  13. Vector(A, G) → secant
  14. Vector(A, E) → cosecant
  15. Line(D, xAxis) → a
  16. Intersect(a, yAxis) → H
  17. Vector(A, H) → sine
  18. Segment(D, H) → b
  19. Line(D, yAxis) → d
  20. Intersect(d, xAxis) → I
  21. Vector(A, I) → cosine
  22. Intersect(yAxis, CotangentAxis) → J
  23. Vector(J, E) → cotangent
  24. Intersect(xAxis, TangentAxis) → K
  25. Vector(K, G) → tangent
  26. Segment(I, D) → e