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Unit Circle Demonstration by Suzanne Doering

Unit Circle Demonstration by Suzanne Doering
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2015-01-12 21:14
CircleTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the geometric properties and trigonometric relationships of the unit circle. It involves core math concepts like the circle, trigonometric functions, special points, angles, and orthogonal lines. Construction highlights include GeoGebra commands such as Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, and CircleArc. Suitable for high school mathematics instruction to understand trigonometric definitions and unit circle applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, θ, A) → B'
  5. Angle(B, A, B') → α
  6. Segment(A, B') → b
  7. OrthogonalLine(B', xAxis) → d
  8. OrthogonalLine(B', xAxis) → a
  9. Intersect(a, xAxis) → C
  10. Segment(A, C) → e
  11. Segment(C, B) → f
  12. Segment(B', C) → g
  13. CircleArc(A, B, B') → k

AI Drawing Prompt Reference

Draw a unit circle starting from the origin, then draw a circle intersecting the x-axis, rotate a point on the circle, calculate the angle, draw a line segment, construct a perpendicular line, find the intersection of the perpendicular line with the x-axis, draw a line segment from the origin to the intersection, then draw a line segment from the intersection to the rotated point, and finally draw a line segment from the rotated point to the intersection, forming part of the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.