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Unit Circle and Cosine Graph by Becky Angus

Unit Circle and Cosine Graph by Becky Angus
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2015-01-03 04:34
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates how to generate the cosine graph using the unit circle. It shows how the x-coordinate of point P on the unit circle varies with angle θ to create the cosine function graph. Key math concepts include the unit circle, trigonometric functions, cosine function, and the relationship between angles and coordinates. Construction involves commands/objects like Point, Rotate, Angle, Segment, Circle, Vector, Sequence, and Function in GeoGebra. Suitable for high school students learning about the generation 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 with point P rotating on it as angle θ changes. Show how the x-coordinate of P varies to create the cosine function graph. Include the unit circle, rotation, angle measurement, coordinate changes, and the cosine function graph's construction.
The prompt above was compiled from the original drawing commands and is for reference only.