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Unit Circle Exact Values Demo

Unit Circle Exact Values Demo
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2019-05-21 03:18
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the exact correspondence between angles and trigonometric values (sin, cos, tan) on the unit circle. It involves core mathematical concepts such as the unit circle, trigonometric functions, angle measurement, and coordinate geometry. Construction highlights include using GeoGebra commands like Intersect (intersection), Point (point), Circle (circle), Segment (line segment), Distance (distance), Angle (angle), Vector (vector), and Polygon (polygon) to draw the unit circle and related shapes. Suitable for high school mathematics teaching to help students visually understand the definition and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → E
  3. Circle(O, E) → c_1
  4. Point(c_1) → X
  5. Segment(O, X) → a
  6. Distance(X, A_1) → b
  7. Angle(E, O, X) → α
  8. Segment(A_1, (x(A_1), 0)) → f
  9. Segment(A_2, (x(A_2), 0)) → g
  10. Segment(B_2, B_1) → h
  11. Segment(C_2, C_1) → i
  12. Vector(O, X) → u
  13. Vector(X, (x(X), 0)) → v
  14. Vector(X, (0, y(X))) → w
  15. Point(u) → A
  16. Segment(A, C_2) → e
  17. Segment(A, B_2) → j
  18. Segment(A, A_2) → k
  19. Segment(A, A_3) → l
  20. Segment(A, B_3) → m
  21. Segment(A, C_3) → n
  22. Segment(A, C_4) → p
  23. Segment(A, B_4) → q
  24. Segment(A, A_4) → r
  25. Segment(A, A_1) → s_1
  26. Segment(A, B_1) → t
  27. Segment(A, C_1) → a_1
  28. Polygon(X, (x(X), 0), A) → poly1, a_2, B, b_1
  29. Polygon((abs(x(X)), abs(y(X))), A, (abs(x(X)), 0)) → poly2, d_1, e_1, a_3

AI Drawing Prompt Reference

Draw a unit circle and mark an angle α starting from the origin O and passing through point X. Then draw a perpendicular line from X to the x-axis, and vectors u, v, and w from point X. Next, mark the points on the unit circle corresponding to the sine and cosine values of angle α, and draw the associated line segments and vectors. Finally, use these points and line segments to construct two polygons.
The prompt above was compiled from the original drawing commands and is for reference only.