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Trigonometric Ratios by tmoorehead

Trigonometric Ratios by tmoorehead
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2015-10-14 02:15
TriangleTrigonometryGeometric Construction
This example demonstrates the concept of trigonometric ratios, including sine, cosine, and tangent. By rotating and constructing line segments, it illustrates how to define these basic trigonometric functions using the relationships between the sides of a triangle. The commands used in the construction include Intersect, Circle, Rotate, Line, Polygon, Angle, Point, and Segment. Suitable for students at the middle school level and above to learn the basic concepts of trigonometric functions and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, Hypotenuse) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, ReferenceAngle, A) → B'
  5. Line(B', yAxis) → a
  6. Intersect(a, xAxis) → C
  7. Polygon(A, B', C) → poly1, Hypotenuse_1, OppositeSide, AdjacentSide
  8. Angle(B', A, C) → β
  9. Point(Circle[D, AdjacentSide]) → E
  10. Segment(D, E) → AdjacentLength
  11. Point(Circle[F, Hypotenuse_1]) → G
  12. Segment(F, G) → HypotenuseLength_1
  13. Point(Circle[H, OppositeSide]) → I
  14. Segment(H, I) → OppositeLength
  15. Angle(B', C, A) → α