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Trigonometric Ratios of 180°+θ

Trigonometric Ratios of 180°+θ
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2015-05-19 10:09
AngleTrigonometryGeometric Construction
This example demonstrates the trigonometric ratios of the angle 180°+θ. The core mathematical concepts involved are trigonometry. Using GeoGebra commands such as Intersect, Circle, Point, etc., a dynamic triangle is constructed where the angle θ can be changed to observe the pattern of its trigonometric ratios. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1.0) → c
  3. Point(c) → P
  4. OrthogonalLine(P, yAxis) → a
  5. Intersect(a, yAxis) → B
  6. Segment(P, B) → b
  7. OrthogonalLine(P, xAxis) → d
  8. Intersect(d, xAxis) → C
  9. Segment(P, C) → e
  10. Segment(A, P) → f
  11. Angle(xAxis, f) → θ
  12. Line(P, A) → i
  13. Intersect(c, i, 2.0) → D
  14. Segment(A, D) → j
  15. Angle(xAxis, j) → α