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Garth's Unit Circle

Garth's Unit Circle
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2016-12-06 11:33
CircleFunctionTrigonometryCoordinate GeometryCalculus
This example demonstrates the construction of a unit circle and its related geometric elements. Core math concepts include circle, unit circle, median value, integral calculus, translation, tree diagrams, and function graphing. It utilizes GeoGebra commands and objects like Intersect, Circle, Point, Line, Segment, Angle, OrthogonalLine, Ray, and Length as per the construction summary. Suitable for high school and above learners to understand geometric properties and calculus applications of the unit circle.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Point(c) → A
  4. Line(A, yAxis) → f
  5. Intersect(f, xAxis) → B
  6. Segment(O, A) → g
  7. Segment(A, B) → h
  8. Segment(B, O) → i
  9. Angle(xAxis, g) → α
  10. Intersect(c, xAxis, 2) → C
  11. OrthogonalLine(C, xAxis) → j
  12. Intersect(c, xAxis, 1) → D
  13. OrthogonalLine(D, xAxis) → k
  14. Intersect(c, yAxis, 2) → E
  15. OrthogonalLine(E, yAxis) → l
  16. Intersect(c, yAxis, 1) → F
  17. OrthogonalLine(F, yAxis) → m
  18. Ray(O, A) → n
  19. Intersect(j, n) → G
  20. Intersect(l, n) → H
  21. Length(G) → Sc
  22. Length(H) → Cs

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with radius 1. From the intersection of the circle with the positive x-axis, draw a vertical line perpendicular to the x-axis. Similarly, from the intersection with the positive y-axis, draw a horizontal line perpendicular to the y-axis. Pick an arbitrary point on the circle, connect it to the origin to form a radius, and draw a line through this point parallel to the y-axis, intersecting the x-axis, thus forming a right triangle. Mark the angle between the radius and the positive x-axis. Then, from the origin, draw a ray passing through the chosen point, intersecting both perpendicular lines, giving two intersection points. Finally, measure and label the distances from the origin to these two intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.