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Trigonometric Function Relationships by Pat Hubeny

Trigonometric Function Relationships by Pat Hubeny
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2015-03-18 21:09
AngleTrigonometryGeometric Construction
This example demonstrates the basic relationships of trigonometric functions. By constructing a triangle, it illustrates the definitions of sine, cosine, and tangent and their interrelationships. GeoGebra commands such as Ray, Point, Segment, Polygon are used for geometric construction. Suitable for students at junior high school level and above to learn trigonometric functions.

GeoGebra Commands & Parameters

  1. Ray(B, B_1) → a_1
  2. Point(a_1) → A
  3. Segment(A, B) → adjacent
  4. OrthogonalLine(B, adjacent) → c_2
  5. Point(c_2) → D
  6. Ray(B, D) → d
  7. Point(d) → C
  8. Polygon(C, A, B) → poly1, b, e, opposite
  9. Angle(B, A, C) → α
  10. Angle(A, C, B) → β
  11. Angle(C, B, A) → γ

AI Drawing Prompt Reference

Draw a right triangle to illustrate the basic relationships of trigonometric functions. Start by drawing the two legs of the right angle. Then, draw a perpendicular line from the right angle vertex to the hypotenuse to get the foot of the altitude. Construct a triangle using the three vertices and the foot of the altitude. Label the three angles and the lengths of the opposite and adjacent sides, and display the corresponding sine, cosine, and tangent values next to them to show their relationships.
The prompt above was compiled from the original drawing commands and is for reference only.