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Sin(x) & Unit Circle - Degrees by Linda Fahlberg-Stojanovska

Sin(x) & Unit Circle - Degrees by Linda Fahlberg-Stojanovska
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2014-01-04 19:29
CircleAngleFunctionTrigonometryGeometric Construction
In collections Trigonometry: Basic and More
This example demonstrates the relationship between an angle α in degrees and the value of sin(α) using the unit circle through an animation. Key math concepts include trigonometric functions, unit circle, angle measurement, and geometric constructions. The construction leverages GeoGebra commands such as Circle, Line, Intersect, Rotate, Angle, Segment, Distance, OrthogonalLine, Midpoint, and Point. It is suitable for high school students or beginners learning about the connection between trigonometric functions and the unit circle, aiding in understanding the definition and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Line(B, O) → a
  3. Intersect(c, a, 2) → C
  4. Rotate(C, α, O) → D
  5. Angle(C, O, D) → β
  6. Segment(O, D) → b
  7. Distance(D, a) → d
  8. OrthogonalLine(D, a) → e
  9. Intersect(a, e) → A_2
  10. Segment(D, A_2) → g
  11. Segment(A_1, D_1) → h
  12. Midpoint(D, A_2) → E
  13. Midpoint(A_1, D_1) → F
  14. Point(xAxis) → G
  15. Segment(G, A_1) → i
  16. Intersect(c, a, 2) → A
  17. Intersect(c, a, 1) → I
  18. Segment(I, A) → j
  19. Intersect(c, j, 2) → J
  20. Segment(O, A_2) → l
  21. Midpoint(O, D) → K

AI Drawing Prompt Reference

Draw a unit circle and mark angle α, showing the sine value by rotating the terminal side of angle α to intersect the unit circle. Include the terminal side of angle α and a perpendicular line, forming a right triangle. Use geometric constructions to demonstrate the relationship between the sine function and the unit circle, suitable for beginners learning trigonometric definitions and properties.
The prompt above was compiled from the original drawing commands and is for reference only.