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Unit Circle and Sine, Cosine, Tangent Functions

Unit Circle and Sine, Cosine, Tangent Functions
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2018-04-27 21:37
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to derive the sine, cosine, and tangent functions from the unit circle. It involves core mathematical concepts such as the unit circle, definitions of trigonometric functions, and the relationship between angles and coordinates. The construction uses GeoGebra commands and objects like Intersect, Point, Circle, Rotate, Segment, Angle, and Distance. It is suitable for high school students learning and understanding the basic definitions and geometric meanings of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Rotate(C, 0, A) → C'
  5. Rotate(C', θ°, A) → P
  6. Segment(P, A) → a
  7. Segment(A, D) → b
  8. Segment(D, P) → d
  9. Angle(P, D, A) → α
  10. Angle((1, 0), (0, 0), P) → β
  11. Distance(A, P) → distanceAP
  12. Distance(A, D) → distanceAD
  13. Distance(D, P) → distanceDP