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Unit Circle: x-axis Symmetry

Unit Circle: x-axis Symmetry
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2014-12-24 02:26
CircleTrigonometryGeometric Construction
In collections Unit Circle Symmetries
This example demonstrates the symmetry of angles α and (360°-α) on the unit circle. The key mathematical concept is trigonometry. Using GeoGebra commands such as circle, rotate, and angle, it illustrates the properties of symmetric angles on the unit circle. Suitable for high school math education.

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 * (2 - 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 centered at the origin with radius 1. Mark the point where the circle intersects the positive x-axis. From the center, draw a radius making an angle α with the positive x-axis, and mark its intersection with the circle; label this angle α with an arc. Then draw another radius making an angle of 360°-α with the positive x-axis, mark its intersection point, and label this angle β with an arc. Connect the center to both intersection points with line segments, and also mark the second intersection of the circle with the x-axis (on the negative side) to show the symmetry of the two angles about the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.