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Animated Sin Cos Tan from Unit Circle

Animated Sin Cos Tan from Unit Circle
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2018-08-18 09:31
CircleAngleTrigonometryGeometric Construction
This example demonstrates the geometric interpretation of sine, cosine, and tangent functions on the unit circle through animation. It involves core math concepts like the unit circle, trigonometric functions, angles, linear equations, and geometric constructions. GeoGebra commands and objects used include Intersect, Circle, Point, Rotate, Angle, Line, OrthogonalLine, and Segment. Suitable for high school mathematics teaching and learning, helping students visually understand the relationship between trigonometric functions and the unit circle, as well as their definitions and properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c_1
  3. Point(xAxis) → B
  4. Rotate(B, θ°, A) → B'
  5. Angle(B, A, B') → α
  6. Intersect(xAxis, yAxis) → O
  7. Line(O, B') → a
  8. Intersect(c_1, a, 2) → P
  9. OrthogonalLine(P, xAxis) → b
  10. Intersect(b, xAxis) → E
  11. Segment(P, E) → d
  12. OrthogonalLine(S, xAxis) → e
  13. Intersect(e, xAxis) → F
  14. Segment(S, F) → f
  15. OrthogonalLine(C, xAxis) → g
  16. Intersect(g, xAxis) → G
  17. Segment(C, G) → h
  18. OrthogonalLine(P, yAxis) → i
  19. Intersect(i, yAxis) → H
  20. Segment(H, P) → j
  21. Intersect(c_1, xAxis, 2) → I
  22. OrthogonalLine(I, xAxis) → k
  23. Intersect(a, k) → J
  24. Segment(J, I) → l
  25. Segment(A, J) → m
  26. OrthogonalLine(D, xAxis) → n
  27. Intersect(n, xAxis) → K
  28. Segment(D, K) → p
  29. Segment(A, P) → q

AI Drawing Prompt Reference

Draw a unit circle on a coordinate plane to illustrate the geometric interpretation of sine, cosine, and tangent functions. Start by marking the intersection of the axes, then draw a unit circle centered at this point. Take a point on the x-axis, rotate it to any angle, and connect it to the center. The intersection of this line with the circle is marked. Draw a perpendicular line from this point to the x-axis, and mark the intersection. Connect these two points. Next, draw a perpendicular from the circle intersection to the y-axis, and mark the intersection. Connect these two points. Combine these points and lines to show the geometric representation of sine, cosine, and tangent functions on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.