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Sine Graph by Roger Lui

Sine Graph by Roger Lui
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2013-04-24 08:16
FunctionTrigonometryCoordinate Geometry
This example demonstrates the generation process of the sine graph. By dragging point P on the unit circle, observe the relationship between the angle and the y-coordinate, and predict the shape of the sine function. Commands used include Point, Segment, Angle, and Text. Suitable for middle school mathematics education.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Segment(P, O) → a
  3. Segment(B, O) → b
  4. Angle(B, O, P) → α
  5. Text("30°") → text1
  6. Text("60°") → text2
  7. Text("90°") → text3
  8. Text("120°") → text4
  9. Text("150°") → text5
  10. Text("180°") → text6
  11. Text("360°") → text7
  12. Text("210°") → text8
  13. Text("240°") → text9
  14. Text("270°") → text10
  15. Text("300°") → text11
  16. Text("330°") → text12
  17. Text("θ = " * α) → text13
  18. Text("P=(" * e * "," * d * ")") → text14
  19. Text("y = sin θ") → text15

AI Drawing Prompt Reference

Draw a unit circle and drag point P on it to observe the relationship between angle α and the y-coordinate of point P. Mark angles such as 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, and 330° on the circle, display the angle α and the coordinates of point P (x, y), and finally show the sine function y = sin θ.
The prompt above was compiled from the original drawing commands and is for reference only.