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Reference Triangles on Standard Plane

Reference Triangles on Standard Plane
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2016-07-18 06:43
AngleTrigonometryTransformation
This example demonstrates how to use reference angles to determine the trigonometric values of any angle. By rotating and constructing, it simplifies the calculation of trigonometric functions. Core concepts include trigonometry, angles, rotation, and parallel lines. GeoGebra commands used include CurveCartesian, Ray, Point, Angle, Polygon, Rotate, and OrthogonalLine. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t), t, 0, θ) → a
  2. Ray(A, B) → b
  3. Point(b) → C
  4. Ray(A, E) → c
  5. Angle(c, b) → α_I
  6. Point(yAxis) → D
  7. Ray(A, D) → d
  8. Point(xAxis) → F
  9. Ray(A, F) → e
  10. Ray(A, G) → f
  11. Angle(b, e) → α_{II}
  12. Angle(e, b) → α_{III}
  13. Angle(b, c) → α_{IV}
  14. Polygon(A, XB, B) → poly1, b_1, a_1, xb
  15. Angle(A, XB, B) → α
  16. Angle(B, XB, A) → β
  17. Rotate(A, θ°, A) → A'
  18. OrthogonalLine(I, xAxis) → j
  19. OrthogonalLine(H, xAxis) → k
  20. OrthogonalLine(J, xAxis) → l
  21. OrthogonalLine(K, xAxis) → m