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Constructing the Unit Circle

Constructing the Unit Circle
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2016-04-18 21:56
CircleTrigonometryGeometric Construction
This example demonstrates the construction of the unit circle, involving concepts such as rational numbers and isosceles triangles. Using GeoGebra commands like Intersect, Circle, and Point, the geometric construction of the unit circle is clearly shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 100) → c
  3. Intersect(c, xAxis, 2) → B
  4. Intersect(c, yAxis, 2) → C
  5. Point(c) → D
  6. Segment(A, D) → a
  7. Segment(A, B) → b
  8. Line(A, B) → d
  9. Line(A, C) → e
  10. OrthogonalLine(D, b) → f
  11. OrthogonalLine(D, e) → g
  12. Intersect(g, e) → E
  13. Intersect(g, f) → F
  14. Intersect(d, xAxis) → G
  15. Intersect(d, xAxis) → H
  16. Intersect(d, b) → I
  17. Intersect(f, d) → J
  18. Segment(D, J) → h
  19. Angle(B, A, D) → α

AI Drawing Prompt Reference

Draw a unit circle with the center at the origin and radius 1. Start by drawing the intersection point A of the x-axis and y-axis, then draw circle c with A as the center. Find the two intersection points B and C of circle c with the x-axis and y-axis, respectively. Choose a point D on circle c and draw segments AD, AB, and AC. Construct the perpendicular line h to AD and the perpendicular line g to DE, and find their intersection points E and F. Use these points and lines to further construct other parts of the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.