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Unit Circle and Cosine Graph by Mario

Unit Circle and Cosine Graph by Mario
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2017-11-02 17:36
CircleFunctionTrigonometry
This example demonstrates generating a cosine graph from the unit circle. It shows the relationship between the rotation of a point on the unit circle and the cosine value. Key mathematical concepts include the unit circle and cosine function. GeoGebra commands used include Point, Rotate, Angle, Circle, Segment, Vector, Sequence, etc. Suitable for high school mathematics 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. Circle(B, A) → c
  8. Segment(B, P) → a
  9. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  10. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  11. Vector((0, 0), (x(Corner[2]), 0)) → z
  12. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  13. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  14. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  15. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  16. Segment(P, Q) → d
  17. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  18. Point(Ray[(0, 0), (-1, 0)]) → B_1
  19. Rotate(A_1, θ, B_1) → P_1
  20. Rotate(A_1, θ, B_1) → A'_2
  21. Rotate(A_1, θ, B_1) → A'_3
  22. Circle(B_1, A_1) → c_1
  23. Segment(B_1, P_1) → a_1
  24. Segment(P, (-1.279, y(P))) → b
  25. Segment(Q, Point[Circle[Q, 0]]) → e

AI Drawing Prompt Reference

Draw a unit circle and plot the cosine graph by rotating a point P on the circle. Start by drawing a point B to the left of the origin, then rotate point A around B to get P and record the angle α. Draw the unit circle c, connect B and P with segment a, and draw the parallel lines u and w to the x-axis and y-axis. Then draw 4 vertical segments from the origin to represent the radius of the unit circle. Next, draw a horizontal line v from B and 4 vertical segments from the origin to represent the cosine values. Finally, draw a perpendicular line b from P to the x-axis and a tangent line e from P to the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.