MathPlotAI Logo MathPlotAI

Unit Circle Demonstration by Mr Friend

Unit Circle Demonstration by Mr Friend
Loading the math board and drawing, please wait…
2016-06-14 20:54
CircleAngleFunctionTrigonometryGeometric Construction
This example dynamically illustrates the relationship between points on the unit circle, angles, and trigonometric values, visually demonstrating the definition of trigonometric functions. Core concepts include the unit circle, trigonometric functions (sine, cosine, tangent), angles, and right triangles. Construction highlights the use of GeoGebra commands and objects like Circle, Point, Segment, Angle, Intersect, and If to create the unit circle, points, segments, angles, and conditional judgments. Suitable for high school mathematics teaching to help students understand the connection between trigonometric functions and the unit circle, enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → circle
  3. Intersect(circle, xAxis, 2) → D
  4. Point(circle) → B
  5. Segment(A, B) → f
  6. Point({x(B), 0}) → C
  7. Segment(A, C) → g
  8. Segment(C, B) → h
  9. Angle(B, A, C) → θ
  10. Angle(A, C, B) → β
  11. Angle(D, A, B) → α
  12. If(tan(α) < 0, "Tan θ : negative", tan(α) ≟ 0, "Tan θ : zero", tan(α) > 0, "Tan θ : positive", Defined[tan(α)] ≟ false, "Tan θ : undefined") → tan_t
  13. If(sin(α) ≟ -1, "Sin θ : -1", -1 < sin(α) < 0, "Sin θ : negative", sin(α) ≟ 0, "Sin θ : zero", 0 < sin(α) < 1, "Sin θ : positive", sin(α) ≟ 1, "Sin θ : 1") → sin_t
  14. If(cos(α) ≟ -1, "Cos θ : -1", -1 < cos(α) < 0, "Cos θ : negative", cos(α) ≟ 0, "Cos θ : zero", 0 < cos(α) < 1, "Cos θ : positive", cos(α) ≟ 1, "Cos θ : 1") → cos_t