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Exact Values on the Unit Circle (Degrees)

Exact Values on the Unit Circle (Degrees)
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2020-06-07 09:47
CircleVectorTrigonometryCoordinate GeometryGeometric Construction
In collections Unit Circle and Radian Defining
This example demonstrates the relationship between angles and trigonometric values (sine, cosine) on the unit circle. Core math concepts include trigonometric functions, unit circle, angle measurement, and geometric construction. It is constructed using GeoGebra commands such as Intersect, Point, Circle, Segment, Distance, Angle, Vector, and Polygon. Suitable for high school students to understand basic properties of trigonometric functions and their geometric interpretations, as well as for visualizing related topics in teaching.

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 in a coordinate system, marking the intersection of the x-axis and y-axis as the origin. Take a point on the circle, connect it to the origin to form a line segment. Then, draw perpendiculars from this point to the x-axis and y-axis, measuring the angle and distance. From this point, draw multiple vectors towards each quadrant and connect these vectors to the boundary points of each quadrant. Finally, connect these points and the origin to form several polygons, illustrating the geometric meaning of trigonometric values.
The prompt above was compiled from the original drawing commands and is for reference only.