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四象限中的三角比

四象限中的三角比
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2019-01-06 10:22
角函数三角函数
本范例展示了四象限中三角比的变化规律。涉及的核心数学概念包括三角函数、角度和象限。通过使用GeoGebra命令如Sequence、Zip、Point等，可以动态地展示角度和三角比的关系。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Sequence(((3 * i))°, i, 1, 120) → angleMeasures
  2. Zip(((5 * cos(A)), (5 * sin(A))), A, angleMeasures) → pointList
  3. Point(pointList) → P
  4. IndexOf(P, pointList) → pIndx
  5. UnicodeToLetter(10007) → xmark
  6. UnicodeToLetter(10003) → cmark
  7. Angle(Vector[(12, 0)], Vector[P]) → angleDisplay
  8. LaTeX("Move point \(P\) and observe the values of the trigonometric ratios.") → SpecInstruc
  9. Segment(P, (x(P), 0)) → VerticalLine
  10. If(x(P) < 0, "-", "") → cosSign
  11. Vector((0, 0), (qWidth, 0)) → hAxis
  12. Rotate(hAxis, π, (0, 0)) → hAxis2
  13. Rotate(hAxis, π / 2, (0, 0)) → vAxis
  14. Rotate(hAxis, (3 * π / 2), (0, 0)) → vAxis2
  15. Segment((0, 0), P) → terminalArm
  16. Zip(Rotate[A, Element[angleMeasures, pIndx], (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPoints
  17. Sequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevron
  18. CurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, Element[angleMeasures, pIndx] / ((2 * π))) → angleCurve
  19. If((y(P) / 5 * 100) ≟ (round(y(P) / 5, 2) * 100), " = ", " \approx ") → sinEquality
  20. LaTeX((((("\text{\sin(\theta) = \dfrac{\(y\)}{\(r\)} = \dfrac{\(" * y(P)) * "\)}{\(5\)}}") * sinEquality) * sinFinalFmt)) → sinStr
  21. If((x(P) / 5 * 100) ≟ (round(x(P) / 5, 2) * 100), " = ", " \approx ") → cosEquality
  22. LaTeX((((("\text{\cos(\theta) = \dfrac{\(x\)}{\(r\)} = \dfrac{\(" * x(P)) * "\)}{\(5\)}}") * cosEquality) * cosFinalFmt)) → cosStr
  23. If(x(P) ≟ 0, "", If[(y(P) / x(P) * 100) ≟ (round(y(P) / x(P), 2) * 100), " = ", " \approx "]) → tanEquality
  24. If(x(P) ≟ 0, "\text{\hphantom{222}undefined}", (("\(" * y(P) / x(P)) * "\)")) → tanFinalFmt
  25. LaTeX((((((("\text{\tan(\theta) = \dfrac{\(y\)}{\(x\)} = \dfrac{\(" * y(P)) * "\)}{\(") * x(P)) * "\)}}") * tanEquality) * tanFinalFmt)) → tanStr
  26. TableText({{thetaStr, radiusStr, sinStr, cosStr, tanStr}}, "vl") → allData
  27. Polygon({(0, 0), (0, 0.5), (0.5, 0.5), (0.5, 0)}) → angleBoxTemplate
  28. Translate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.5, x(P)], If[y(P) > 0, 0, -0.5])) → angleBox