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Unit Circle and Trigonometric Functions by Jesse Parete

Unit Circle and Trigonometric Functions by Jesse Parete
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2012-06-05 04:43
CircleFunctionTrigonometry
This example demonstrates trigonometric relationships using a unit circle. As a point moves around the circle, the graphs of sine and cosine functions change accordingly. The construction involves commands like Circle, Point, Tangent, Segment, Vector, Angle, etc. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Tangent(C, c) → a,
  5. Segment(A, C) → b
  6. OrthogonalLine(C, xAxis) → d
  7. Intersect(d, xAxis) → D
  8. Segment(C, D) → e
  9. OrthogonalLine(C, yAxis) → f
  10. Intersect(f, yAxis) → E
  11. Segment(C, E) → g
  12. Intersect(c, xAxis) → G, H
  13. Point(c) → O
  14. CircumcircleArc(G, O, C) → q
  15. Point(b) → F
  16. Vector(A, F) → u
  17. Point(b) → I
  18. Angle(u) → θ
  19. Intersect(b, g) → L
  20. Text(" " + (x(L))) → text10
  21. Point(g) → J
  22. Point(e) → K
  23. Text(" " + (y(L))) → text11

AI Drawing Prompt Reference

Draw a unit circle and show the sine and cosine values as a point moves around it. Start by drawing the coordinate axes, then draw a unit circle centered at the origin. Next, pick a point on the circle and draw a tangent line and a segment from the origin to this point. Draw lines perpendicular to the x-axis and y-axis through this point, and find their intersections with the axes. Then, draw segments from the origin to these intersection points. Finally, draw an arc of the circle intersecting the x-axis, representing the angle.
The prompt above was compiled from the original drawing commands and is for reference only.