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Unit Circle and Cosine Graph by Anthony OR 柯志明

Unit Circle and Cosine Graph by Anthony OR 柯志明
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2012-04-17 20:47
CircleFunctionTrigonometry
In collections Trigonometric Graphs and the Unit Circle Trigonometric Graphs and the Unit Circle wellington point The Unit Circle Begins Trigonometric Graphs and the Unit Circle Trigonometric Graphs
This example generates the cosine graph using the unit circle. It demonstrates how the movement of a point on the unit circle corresponds to changes in the cosine value. Key mathematical concepts include trigonometry and coordinate geometry. GeoGebra commands used include Point, Rotate, Angle, Segment, Circle, Vector, Sequence, etc. Suitable for high school math education and learning.

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. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  18. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  19. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  20. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  21. Segment(Q, (0, y(Q))) → d
  22. Point(Ray[(0, 0), (-1, 0)]) → B_1
  23. Rotate(A_1, θ, B_1) → P_1
  24. Rotate(A_1, θ, B_1) → A'_2
  25. Rotate(A_1, θ, B_1) → A'_3
  26. Circle(B_1, A_1) → c_1
  27. Segment(B_1, P_1) → a_1

AI Drawing Prompt Reference

Draw a unit circle and move a point on it to show the correspondence between the point and the cosine function graph. Start by plotting the coordinate axes and origin, then draw the unit circle. Mark a point on the circle and rotate it as the angle changes, connecting the point to the center of the circle and displaying its corresponding cosine value. Finally, project the point on the circle onto the x-axis and y-axis to form the cosine function graph, clearly showing the relationship between the unit circle and the cosine function.
The prompt above was compiled from the original drawing commands and is for reference only.