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Unit Circle and Trigonometric Ratios by Ella Sayin

Unit Circle and Trigonometric Ratios by Ella Sayin
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2016-05-18 00:26
CircleAngleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric ratios (sine, cosine) while showing the distribution of angles across different quadrants. Core concepts include the unit circle, trigonometric functions (sine, cosine), quadrant relationships, and angle measurement. Construction involves GeoGebra commands such as Intersect, Segment, Rotate, Angle, Name, and OrthogonalLine. Suitable for high school mathematics to understand the geometric connection between the unit circle and trigonometric functions, as well as quadrant properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Intersect(c, xAxis, 2) → B
  3. Segment(A, B) → a
  4. Rotate(B, θ_1, A) → B'
  5. Segment(B', A) → b
  6. Rotate(B, θ_1, A) → B'_1
  7. Angle(B, A, B'_1) → θ
  8. Name(θ) → A1
  9. OrthogonalLine(B', a) → d
  10. Intersect(d, a) → C
  11. Segment(B', C) → e
  12. OrthogonalLine(B', yAxis) → g
  13. Intersect(g, yAxis) → D
  14. Segment(D, B') → h