MathPlotAI Logo MathPlotAI

Forming a Sine Graph

Forming a Sine Graph
Loading the math board and drawing, please wait…
2015-12-29 11:06
FunctionTrigonometryCoordinate Geometry
This example demonstrates the formation of a sine graph. Key mathematical concepts include the sine function, angles, and vectors. Using GeoGebra commands such as Point, Rotate, and Intersect, the example dynamically illustrates the properties of the sine function. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Rotate((-1, 0), θ, A) → P
  3. Intersect(xAxis, yAxis) → O
  4. Vector(A - (1.2, 0), A + (1.2, 0)) → u_A
  5. Vector(A - (0, 1.2), A + (0, 1.2)) → v_A
  6. Vector((0, -3), (0, 3)) → V_O
  7. Sequence(Segment[A + ((0.5 * k) - 1, 0), A + ((0.5 * k) - 1, -0.05)], k, 0, 4) → list_uA
  8. Sequence(Segment[A + (0, (0.5 * k) - 1), A + (-0.05, (0.5 * k) - 1)], k, 0, 4) → list_vA
  9. Sequence(Segment[O + ((π / 2 * k), 0), O + ((π / 2 * k), -0.05)], k, 0, 4) → list_uO
  10. Sequence(Segment[O + (0, (0.5 * k) - 1), O + (-0.05, (0.5 * k) - 1)], k, 0, 4) → list_vO
  11. Circle(A, 1) → c
  12. Angle((-1, 0), A, P) → α
  13. Segment(A, P) → r
  14. Vector((-0.5, 0), (7, 0)) → u_O
  15. Segment(P, B) → b
  16. Segment(I, G) → d
  17. Segment(G, H) → e
  18. Segment(J, K) → f
  19. Segment(L, K) → g
  20. Segment(Q, B) → i
  21. Line(P, x = 0) → k
  22. Line(A, y = 1) → l
  23. Intersect(k, l) → S
  24. Segment(P, S) → m
  25. Angle((-1, 0), A, P) → γ