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Unit Circle and Trig Ratios

Unit Circle and Trig Ratios
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2018-05-16 03:06
CircleAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the unit circle in both radians and degrees with the reference angle highlighted in orange. It involves core math concepts like the unit circle, trigonometric ratios, reference angles, and angle-degree conversion. Construction highlights GeoGebra commands such as Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, Text, FractionText, and objects like Slider, points, and text elements. Suitable for high school mathematics education to understand the definition of trigonometric functions in relation to the unit circle, ideal for exploratory learning by students.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis) → C, D
  4. Rotate(D, α, A) → D'
  5. Angle(D, A, D') → β
  6. Segment(A, D') → a
  7. Angle(D', A, C) → γ
  8. Angle(D', A, D) → δ
  9. OrthogonalLine(D', xAxis) → b
  10. Intersect(b, xAxis) → F
  11. Segment(D', F) → d
  12. Segment(E, F) → e
  13. Text(θ) → text1
  14. Text(x(D')) → text3
  15. Text(y(D')) → text4
  16. FractionText(θ) → text5
  17. Angle(D', E, F) → ε