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Tracing Sine and Cosine Functions

Tracing Sine and Cosine Functions
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2016-07-16 16:04
FunctionTrigonometryGeometric Construction
This example demonstrates the process of tracing sine and cosine functions. Key mathematical concepts include trigonometric functions. Using GeoGebra commands such as Intersect, Point, Angle, etc., the generation of function graphs can be intuitively understood. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Intersect(c, xAxis, 2) → B
  3. Point(c) → C
  4. Angle(B, A, C) → α
  5. OrthogonalLine(C, xAxis) → f
  6. Segment(A, C) → g
  7. Intersect(f, xAxis) → D
  8. Segment(C, D) → h
  9. OrthogonalLine(C, yAxis) → i
  10. Intersect(i, yAxis) → E
  11. Segment(C, E) → j
  12. Segment(A, D) → k
  13. Segment(E, A) → l
  14. CircleArc(A, B, C) → e
  15. OrthogonalLine(F, xAxis) → m
  16. Intersect(m, xAxis) → G
  17. Segment(F, G) → n
  18. OrthogonalLine(F, xAxis) → p
  19. Segment(F, H) → r

AI Drawing Prompt Reference

Draw a coordinate system with x and y axes. Mark the origin, take a point to the right on the x-axis, connect this point to the origin, draw a circle with this point as the center, intersecting the x-axis at another point. Connect these two points, draw a line perpendicular to the x-axis through the center, intersecting the x-axis at a point. Connect the center to this point. Draw a line perpendicular to the y-axis through the center, intersecting the y-axis at a point. Connect the center to this point. Finally, draw an arc connecting the origin and the center, and two line segments from the center and the origin perpendicular to the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.