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Unit Circle Exact Values

Unit Circle Exact Values
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2019-08-21 06:02
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the exact trigonometric values (sin, cos, tan) corresponding to angles on the unit circle. It involves core math concepts like the unit circle, trigonometric functions, rotation angles, and coordinate geometry. Construction highlights include commands like Intersect, Point, Circle, Segment, Distance, Angle, Vector, and Polygon, as listed in the summary. Suitable for high school students learning trigonometric properties and analytical geometry applications.

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 a point X on it. Draw a line segment a from the center O to point X, and measure the length b and angle α of line segment OX. Then, draw a perpendicular from point X to the x-axis, and vectors u, v, and w. Draw vector u from point O and mark point A on the x-axis. Finally, draw multiple line segments from point A to form polygons representing sine, cosine, and tangent values.
The prompt above was compiled from the original drawing commands and is for reference only.