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Trigonometric Ratios Demo by Toh Wee Teck

Trigonometric Ratios Demo by Toh Wee Teck
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2013-07-27 17:07
AngleTrigonometryGeometric Construction
This example demonstrates the geometric meaning of trigonometric ratios (sine, cosine, tangent) in right-angled triangles. It involves core concepts like the definition of trigonometric functions, properties of right triangles, and angle measurement. The construction uses GeoGebra commands such as Line, Point, OrthogonalLine, Segment, and Angle to build the triangle and label key elements. Suitable for high school mathematics teaching to help students visually understand the relationship between trigonometric functions and triangle sides/angles.

GeoGebra Commands & Parameters

  1. Line(A, Z) → a
  2. Point(a) → B
  3. OrthogonalLine(B, a) → b
  4. Point(b) → C
  5. Segment(A, B) → AB
  6. Segment(B, C) → BC
  7. Segment(C, A) → AC
  8. Angle(B, A, C) → θ
  9. Angle(C, B, A) → β
  10. Segment(A, B) → m
  11. Segment(A, C) → n

AI Drawing Prompt Reference

Draw a right triangle, label the two legs and the hypotenuse, and mark one acute angle. Then measure and display the lengths of the two legs and the hypotenuse. Finally, visually demonstrate the relationships that the sine value equals the opposite side over the hypotenuse, the cosine value equals the adjacent side over the hypotenuse, and the tangent value equals the opposite side over the adjacent side.
The prompt above was compiled from the original drawing commands and is for reference only.