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Sine and Cosine Animation Demo

Sine and Cosine Animation Demo
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2017-04-25 06:31
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the geometric meaning of sine and cosine values on the unit circle, involving core concepts like trigonometric functions, unit circle, angle rotation, and coordinate system. It utilizes GeoGebra commands and objects such as Point, Circle, Rotate, Angle, Segment, OrthogonalLine, Intersect with objects like θ, A, B, C, α. Suitable for high school mathematics teaching to understand trigonometric function graphs, properties, and parametric equations application.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Circle(B, C) → c
  3. Rotate(C, θ, B) → C'
  4. Angle(C, B, C') → α
  5. Segment(C, B) → f
  6. Segment(B, C') → g
  7. OrthogonalLine(C', xAxis) → h
  8. Intersect(h, xAxis) → D
  9. Segment(D, C') → i
  10. OrthogonalLine(A, xAxis) → j
  11. Intersect(j, xAxis) → E
  12. Segment(A, E) → k
  13. Segment(B, D) → l
  14. Segment(E, F) → m
  15. Intersect(i, l) → G

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. From point B on the circle, draw a perpendicular to the x-axis, meeting it at D. Rotate point B by angle θ to get point C' on the circle. Connect B to C' and B to C, labeling these segments f and g respectively. Draw a line perpendicular to the x-axis through C', meeting it at E. Connect the origin A to E and draw a perpendicular to the x-axis through A, meeting it at F. Connect E to F, and mark the intersection of this line with segment BC as point G.
The prompt above was compiled from the original drawing commands and is for reference only.