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Unit Circle and Trig Ratios Demo

Unit Circle and Trig Ratios Demo
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2016-03-01 05:30
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between any point on the unit circle and its corresponding trigonometric values (sine, cosine). It involves core mathematical concepts such as the unit circle, trigonometric functions, right triangles, angles, and vectors. The construction uses GeoGebra commands like Intersect, Point, Circle, Segment, OrthogonalLine, Angle, Distance, and Slope to build the unit circle, axes, trigonometric lines, and annotations. Suitable for high school students and learners needing a visual understanding of the connection between trigonometric functions and the unit circle.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → a
  6. OrthogonalLine(C, xAxis) → b
  7. Intersect(b, xAxis) → D
  8. Angle(D, A, C) → α
  9. Distance(C, D) → distanceCD
  10. Distance(D, A) → distanceDA
  11. Distance(A, C) → distanceAC
  12. Slope(a) → tangent