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Primary Trigonometric Ratios

Primary Trigonometric Ratios
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2014-02-12 12:46
AngleTrigonometryGeometric Construction
This example demonstrates the relationships between side lengths and angles in right triangles, focusing on primary trigonometric ratios (sine, cosine, tangent). Key math concepts include the definition of trigonometric functions, geometric properties of right triangles, and side-angle relationships. GeoGebra commands and objects used in construction are Rotate, Angle, Line, Point, Polygon, and Distance, such as rotating to construct special points, measuring sides and angles, and drawing geometric figures. Suitable for middle school and above students to understand basic trigonometric definitions and practical applications.

GeoGebra Commands & Parameters

  1. Rotate(F, 90*°, C) → A'
  2. Angle(F, C, A') → α
  3. Line(C, A') → a_2
  4. Point(a_2) → B
  5. Line(C, F) → b_2
  6. Point(b_2) → A
  7. Polygon(B, C, A) → poly1, a_1, b_1, c_1
  8. Angle(B, A, C) → β
  9. Angle(C, B, A) → γ
  10. Distance(A, B) → c
  11. Distance(A, C) → b
  12. Distance(B, C) → a

AI Drawing Prompt Reference

Draw a right triangle and label the three angles and corresponding side lengths, showing the geometric meaning of the three primary trigonometric ratios. First, construct a right triangle, then rotate one vertex by 90 degrees to get another vertex. Measure and label the sizes of the three angles and the lengths of the three sides, and finally represent the geometric relationships of sine, cosine, and tangent values with shapes.
The prompt above was compiled from the original drawing commands and is for reference only.