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Unit Circle Development - Part 3

Unit Circle Development - Part 3
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2017-10-18 08:26
CircleAngleFunctionTrigonometryGeometric Construction
In collections Introduction to Radians and the Unit Circle
This example demonstrates the geometric construction of the unit circle and the visualization of related angle measures and trigonometric values. Core mathematical concepts include the unit circle, trigonometric functions, angle measurement, and geometric construction. GeoGebra commands and objects used in the construction are Intersect (intersection), Segment (line segment), Rotate (rotation), Angle (angle measure), OrthogonalLine (perpendicular line), and SurdText (radical text). Suitable for high school mathematics education, helping students intuitively understand the relationship between trigonometric functions and the unit circle, and enhancing geometric construction skills.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 1) → D
  2. Intersect(xAxis, yAxis) → α
  3. Intersect(c, xAxis, 2) → A
  4. Segment(D, A) → i
  5. Rotate(A, angle, α) → B
  6. Segment(α, A) → f_1
  7. Angle(A, α, B) → β
  8. Segment(α, B) → g_1
  9. OrthogonalLine(B, i) → h
  10. Intersect(h, i) → C
  11. Segment(B, C) → g
  12. Angle(B, C, α) → γ
  13. Angle(α, B, C) → δ
  14. Segment(α, C) → f
  15. SurdText(cos(β)) → text2
  16. SurdText(sin(β)) → text3
  17. Intersect(c, yAxis, 2) → E
  18. Intersect(c, yAxis, 1) → F