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Unit Circle by El Mostafa Kalmoun

Unit Circle by El Mostafa Kalmoun
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2019-02-04 17:19
CircleTrigonometryCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates the construction of the unit circle and its relationship with trigonometric functions. Key math concepts include circle, coordinate geometry, trigonometry, and vectors. Construction highlights the use of GeoGebra commands like Intersect, Circle, Mirror, Point, Segment, Angle, OrthogonalLine, and Line. Suitable for high school mathematics teaching to understand trigonometric definitions and applications of coordinate geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Mirror(B, yAxis) → B'
  4. Mirror(B, xAxis) → B'_1
  5. Mirror(B', xAxis) → B''
  6. Mirror(C, yAxis) → C'
  7. Mirror(C', xAxis) → C''
  8. Mirror(C'', yAxis) → C'''
  9. Mirror(D, yAxis) → D'
  10. Mirror(D', xAxis) → D''
  11. Mirror(D'', yAxis) → D'''
  12. Point(c) → I
  13. Segment(I, A) → g
  14. Angle(E, A, I) → α
  15. OrthogonalLine(I, xAxis) → h
  16. Intersect(h, xAxis) → Q
  17. Line(A, Q) → i
  18. Segment(I, Q) → j
  19. Segment(A, Q) → k

AI Drawing Prompt Reference

Draw a unit circle and demonstrate its relationship with trigonometric functions. Start by plotting the origin and drawing a circle centered at the origin with a radius of 1. Mirror points on the circle across the x-axis and y-axis multiple times to create symmetric points around the circle. Connect the origin to these points to form line segments. Draw perpendicular lines from the points on the circle to the x-axis, marking the feet of the perpendiculars. Connect the origin to these feet to form additional line segments. Finally, label the angles and segments clearly to illustrate the definitions of trigonometric functions and the applications of coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.