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Cosine Graph from Unit Circle by Sam Waterfield

Cosine Graph from Unit Circle by Sam Waterfield
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2018-02-08 05:08
CircleFunctionTrigonometryCoordinate GeometryGraphing
This example dynamically demonstrates the relationship between the x-coordinate of a point on the unit circle and the cosine curve, revealing the geometric meaning of the cosine function. Core math concepts include the unit circle, trigonometric functions, coordinate geometry, and function graphs. Construction highlights use GeoGebra commands/objects like Point, Rotate, Angle, Segment, Circle, Vector, Sequence, and Function. Suitable for high school mathematics teaching to help students visually understand the generation process of trigonometric function graphs.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Rotate(A, θ, B) → A'
  4. Angle(A, B, A') → α
  5. Rotate(A, θ, B) → A'_1
  6. Angle(A, B, A'_1) → β
  7. Segment(Q, (x(Q), 0)) → e
  8. Segment((0, 0), (x(Q), 0)) → g
  9. Circle(B, A) → c
  10. Segment(B, P) → a
  11. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  12. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  13. Vector((0, 0), (x(Corner[2]), 0)) → z
  14. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  15. Segment(B, (x(P), 0)) → b
  16. Segment(P, (x(P), 0)) → h
  17. Function(cos((120° * x)), 0, x(Q)) → f
  18. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  19. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  20. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  21. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  22. Segment(Q, (0, y(Q))) → d
  23. Point(Ray[(0, 0), (-1, 0)]) → B_1
  24. Rotate(A_1, θ, B_1) → P_1
  25. Rotate(A_1, θ, B_1) → A'_2
  26. Rotate(A_1, θ, B_1) → A'_3
  27. Circle(B_1, A_1) → c_1
  28. Segment(B_1, P_1) → a_1

AI Drawing Prompt Reference

Draw a unit circle and drop a perpendicular from point P on the circle to the x-axis to form angle α. Rotate point A to form points P and A', and draw angle β. Take point Q on the x-axis and draw a vertical line from Q to the unit circle to form segment e. Draw tangent segment a from the unit circle to the x-axis and draw unit vectors u and w on the x-axis. Draw an arc segment f from the x-axis to the unit circle to represent the cosine function. Draw diameter segment v of the unit circle and draw grid segments list2 and list3 on the y-axis and grid segments list4 on the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.