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Unit Circle by Will Elliott

Unit Circle by Will Elliott
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2017-02-17 00:18
CircleTrigonometryGeometric Construction
This example demonstrates the unit circle and its trigonometric relationships. Key mathematical concepts include circle and trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant). Constructed using GeoGebra commands such as rotation, tangent, ray, etc., it is suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, Angle°, A) → C
  5. Angle(B, A, C) → α
  6. Tangent(C, c) → a, b
  7. Intersect(a, xAxis) → D
  8. Intersect(a, yAxis) → E
  9. Ray(A, C) → d
  10. Segment(E, C) → cotθ
  11. Segment(C, D) → tanθ
  12. Segment(A, D) → secθ
  13. Segment(E, A) → cscθ
  14. OrthogonalLine(C, xAxis) → i
  15. OrthogonalLine(C, yAxis) → j
  16. Intersect(yAxis, j) → F
  17. Intersect(i, xAxis) → G
  18. Segment(F, C) → cosθ
  19. Segment(G, C) → sinθ

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a radius of 1. Find the intersection of the x-axis and y-axis as point A, and draw the unit circle c with A as the center. Find the intersection of circle c and the x-axis as point B, and rotate point B around point A to form point C. Measure the angle BAC as α. Draw the tangents a and b from point C, intersecting the x-axis at D and the y-axis at E. Draw a ray from A through C, and draw line segments from C to D (tanθ), C to E (cotθ), C to A (secθ), and C to the origin (cscθ). Draw perpendicular lines i and j from point C to the y-axis and x-axis, intersecting at F and G, and draw line segments from F to C (cosθ) and G to C (sinθ).
The prompt above was compiled from the original drawing commands and is for reference only.