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Sine Ratio

Sine Ratio
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2018-10-19 01:43
TriangleTrigonometryCoordinate Geometry
This example demonstrates the concept of the sine ratio. By constructing angles and side lengths in a triangle, students can visually understand the definition and application of the sine ratio. GeoGebra commands used include Element, Point, Polygon, LaTeX, UnicodeToLetter, Angle, Join, TableText, and Length. Suitable for middle school and above students learning trigonometry.

GeoGebra Commands & Parameters

  1. Element(RatioLst, caseIndx) → currRatio
  2. Point(Segment[(1, 0), (26, 0)]) → B
  3. Point(Segment[(x(B), 0), (x(B), 13)]) → C
  4. Polygon(C, A, B) → t1, b, c, a
  5. LaTeX(If[isCorrect ∧ a ≠ 3, "=\dfrac{4}{5}", ""]) → correctCos
  6. LaTeX(If[isCorrect ∧ a ≠ 3, "=\dfrac{3}{5}", ""]) → correctSin
  7. LaTeX(If[IsInteger[lenHyp], (("" * lenHyp) * ""), (("\sqrt{" * bSq) * "}")]) → hypTxt
  8. UnicodeToLetter(10007) → xmark
  9. UnicodeToLetter(10003) → cmark
  10. Angle(C, B, A) → α
  11. Polygon(A, B, C) → t2, c_1, a_1, b_1
  12. LaTeX("A") → lblA
  13. LaTeX("C") → lblC
  14. LaTeX("B") → lblB
  15. Join({titleLst, Zip[{x(A), y(A)}, A, triList]}) → fullList
  16. TableText(fullList, "|111_111111111111l") → triTable
  17. Angle(B, A, C) → θ
  18. LaTeX("\dfrac{3}{5}") → A4
  19. Length(RatioLst) → numCases
  20. Element(RatioFormatedLst, caseIndx) → currRatioDisp
  21. LaTeX((("\text{\textbf{Question: }How many right-triangles can you construct with \sin(\theta ) = \frac{opp}{hyp}=" * currRatioDisp) * " ?\\What is the value of \cos(\theta ) = \frac{adj}{hyp} for these triangles?} ")) → MainInstruc
  22. LaTeX("\dfrac{5}{13}") → C4
  23. LaTeX("\dfrac{4}{5}") → B4
  24. LaTeX("\text{\textbf{Instructions: }Drag vertex \(C\) up and down to change the height of the triangle, and slide \\vertex \(B\) left and right to change the width of the triangle.}") → SpecInstruc
  25. TableText({ratioData}, "v") → RatioTable

AI Drawing Prompt Reference

Create a diagram of a right triangle to illustrate the sine ratio. The triangle has a horizontal base with one vertex that can be slid left and right along the base to change the width, and another vertex that can be dragged up and down to adjust the height. Label the angles θ and α, and display the sine ratio as a fraction (e.g., 3/5) and the cosine ratio. Include a table showing ratio data for various triangle configurations. Add instructional text guiding the user to drag the vertices to explore right triangles with a constant sine ratio and determine the corresponding cosine ratio.
The prompt above was compiled from the original drawing commands and is for reference only.