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Mapping Special Right Triangles on the Unit Circle

Mapping Special Right Triangles on the Unit Circle
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2015-03-09 22:12
TriangleCircleTrigonometryCoordinate Geometry
This example demonstrates the mapping of special right triangles on the unit circle to investigate the relationship between their x and y coordinates and sine and cosine. It uses commands such as Intersect, Circle, Segment, Distance, Angle, Vector, and Polygon. Suitable for students learning trigonometry and coordinate geometry.

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 special right triangle on the unit circle. Start by drawing the intersection point O of the x-axis and y-axis, then draw a circle c_1 with O as the center and OE as the diameter. Next, take a point X on the circle and draw line segment a from O to X, measure the distance b from X to A1, and calculate the angle α between EO and X. Then draw horizontal line f and vertical line g from X to A1, and line segments h, i from X to A2, B2, C2. Draw vector OX, horizontal line v, and vertical line w from X to A1, then draw point A, and connect A to C2, B2, A2, A3, B3, C3, A4, B4, C4, A1, B1, and C1. Finally, draw two polygons: one with vertices X, A1, A, and another with vertices A1, A, A1.
The prompt above was compiled from the original drawing commands and is for reference only.