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Unit Circle Origin Symmetry

Unit Circle Origin Symmetry
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2014-12-24 02:18
CircleTrigonometryGeometric Construction
In collections Unit Circle Symmetries
This example demonstrates the symmetry of angles α and 180°+α about the origin in the unit circle. Key math concepts include trigonometry, unit circle, and symmetry. It is constructed using GeoGebra commands like Intersect, Point, Circle, Rotate, Angle, and Segment, making it suitable for high school mathematics instruction on understanding the symmetric properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, (a * π / 180), A) → P_1
  5. Angle(B, A, P_1) → α
  6. Intersect(c, xAxis, 2) → B'
  7. Rotate(B, (π * (1 + a / 180)), A) → P_2
  8. Segment(A, P_2) → b
  9. Segment(A, P_1) → d
  10. Angle(B, A, P_2) → β

AI Drawing Prompt Reference

Draw a unit circle in a coordinate system, mark the intersection point of the circle's center with the x-axis, draw a line segment from this point to the circle as angle α, then construct the symmetric angle of α (180°+α) and label the vertices and terminal sides of both angles, finally connect the center of the circle to the terminal sides of both angles to show symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.