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MT4-01-P3b-XT1 Trig Ratios Interactive Practice

MT4-01-P3b-XT1 Trig Ratios Interactive Practice
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2019-01-04 20:35
AngleFunctionTrigonometrySlider AnimationGraphing
① This interactive GeoGebra example demonstrates trigonometric ratios (sine, cosine, tangent) in a right triangle, with a slider to change the angle and observe real-time updates of the ratios and their graphs. ② Core math concepts include definitions of trigonometric functions, angle measurement in degrees/radians, relationships between sides and angles, and the connection between numeric tables and function plots. ③ Construction uses GeoGebra commands such as Point, Segment, Polygon to build the triangle, Angle and LaTeX for labeling, Slider for dynamic angle control, TableText and Sequence for generating value tables, CurveCartesian for plotting trig curves, Zip and If for conditional logic, and Vector/Translate for auxiliary transformations. ④ Suitable for high school or introductory college students learning trigonometry, as well as teachers for classroom demonstrations or self-paced exploration, helping learners grasp how trig ratios vary with angle.

GeoGebra Commands & Parameters

  1. Point(validPoints) → P
  2. IndexOf(P, validPoints) → currRow
  3. Join({Sequence["black", i, 1, currRow - 1], {"#d32f2f"}, Sequence["black", i, currRow + 1, Max[13, maxRadius + 1]]}) → RowColours
  4. Angle((5, 0), (0, 0), P) → angleTheta
  5. LaTeX("(4,3)") → B3
  6. LaTeX("(0,5)") → B5
  7. LaTeX("(-4,3)") → B7
  8. LaTeX("(-3,-4)") → B10
  9. LaTeX("(0,-5)") → B11
  10. LaTeX("(3,-4)") → B12
  11. LaTeX("(4,-3)") → B13
  12. LaTeX("(5,0)") → B14
  13. Sequence(If[i ≟ 1, (("\cellcolor{#ffcc80}{\text{" * B1) * "}}"), If[currRow ≠ i - 1, Element[B1:B14, i], (("\cellcolor{#fff59d}{" * Element[B1:B14, i]) * "}")]], i, 1, maxRow + 1) → tblColPoints
  14. Sequence(If[i ≟ 1, (("\cellcolor{#ffcc80}{" * C1) * "}"), If[currRow ≠ i - 1, Element[C1:C14, i], (("\cellcolor{#fff59d}{" * Element[C1:C14, i]) * "}")]], i, 1, maxRow + 1) → tblColSin
  15. Sequence(If[i ≟ 1, (("\cellcolor{#ffcc80}{" * D1) * "}"), If[currRow ≠ i - 1, Element[D1:D14, i], (("\cellcolor{#fff59d}{" * Element[D1:D14, i]) * "}")]], i, 1, maxRow + 1) → tblColCos
  16. Element(B2:B14, currRow) → currPt
  17. Segment(P, (x(P), 0)) → verticalSegment
  18. Sequence(If[i ≟ 1, (("\cellcolor{#ffcc80}{" * F1) * "}"), If[currRow ≠ i - 1, Element[F1:F14, i], (("\cellcolor{#fff59d}{" * Element[F1:F14, i]) * "}")]], i, 1, maxRow + 1) → tblColTheta
  19. Sequence(If[i ≟ 1, (("\cellcolor{#ffcc80}{" * E1) * "}"), If[currRow ≠ i - 1, Element[E1:E14, i], (("\cellcolor{#fff59d}{" * Element[E1:E14, i]) * "}")]], i, 1, maxRow + 1) → tblColTan
  20. TableText({tblColTheta, tblColPoints, tblColSin, tblColCos, tblColTan}, "|11111_11111111111111v") → tblData
  21. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  22. Zip(Rotate[A, angleTheta, (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPoints
  23. Sequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevron
  24. CurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, angleTheta / (360°)) → angleCurve
  25. Vector((0, 0), Rotate[(6.5, 0), angleTheta]) → terminalVector
  26. If(x(P) > 0, If[y(P) ≥ 0, P + (1, 0.5), P + (1.4, -2)], If[y(P) > 0, P + (-3, 1), P + (-4, -2.5)]) → Ppos
  27. Polygon({(0, 0), (0.7, 0), (0.7, 0.7), (0, 0.7)}) → angleBoxTemplate
  28. Translate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.7, x(P)], If[y(P) > 0, 0, -0.7])) → angleDecoration
  29. LaTeX(("P" * currPt)) → txtPtP