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Unit Circle: y-axis Symmetry

Unit Circle: y-axis Symmetry
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2014-12-24 02:07
CircleTrigonometryCoordinate GeometryGeometric Construction
In collections Unit Circle Symmetries
This example demonstrates the symmetry of angles α and 180°-α about the y-axis on the unit circle. It involves core trigonometric concepts and uses GeoGebra commands like Intersect, Point, Circle, Rotate, Angle, and Segment for construction. Suitable for high school mathematics education to understand trigonometric properties and symmetry.

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 with the x-axis, and draw a line segment representing angle α from this point to the circle. Then, create the symmetric line segment of α about the y-axis to show the angle 180°-α, labeling both angles and their corresponding line segments to illustrate the y-axis symmetry on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.