互余三角比

互余三角比
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2019-02-06 00:08
本范例演示互余三角比的概念。通过构造角度和三角函数值,帮助学生理解正割、余割等互余三角比的性质。使用了Sequence, Zip, Point等GeoGebra命令,适合高中数学教学。

GeoGebra 命令及参数

  1. Sequence(i, i, 0, 357, 3) → angleMeasures
  2. Zip(((5 * cos(A°)), (5 * sin(A°))), A, angleMeasures) → pointList
  3. Point(pointList) → P
  4. IndexOf(P, pointList) → currIndx
  5. If(x(P) ≠ 0, 5 / x(P)) → D4
  6. UnicodeToLetter(10007) → xmark
  7. UnicodeToLetter(10003) → cmark
  8. Segment(P, (x(P), 0)) → VerticalLine
  9. Vector((0, 0), (qWidth, 0)) → hAxis
  10. Rotate(hAxis, π, (0, 0)) → hAxis2
  11. Rotate(hAxis, π / 2, (0, 0)) → vAxis
  12. Rotate(hAxis, (3 * π / 2), (0, 0)) → vAxis2
  13. Element(angleMeasures, currIndx) → currAngle
  14. Zip(Rotate[A, currAngle°, (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPoints
  15. Sequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevron
  16. If((5 / y(P) * 100) ≟ (round(5 / y(P), 2) * 100), " = ", " \approx ") → cscEquality
  17. If(y(P) ≟ 0, "\text{undefined}", (("\(" * 5 / y(P)) * "\)")) → cscFinalFmt
  18. LaTeX(((((("\text{\csc(\theta) = \dfrac{\(r\)}{\(y\)} = \dfrac{\(5\)}{\(" * y(P)) * "\)}") * cscEquality) * cscFinalFmt) * "}")) → cscStr
  19. If((5 / x(P) * 100) ≟ (round(5 / x(P), 2) * 100), " = ", " \approx ") → secEquality
  20. If(x(P) ≟ 0, "\text{undefined}", (("\(" * 5 / x(P)) * "\)")) → secFinalFmt
  21. LaTeX(((((("\text{\sec(\theta) = \dfrac{\(r\)}{\(x\)} = \dfrac{\(5\)}{\(" * x(P)) * "\)}") * secEquality) * secFinalFmt) * "}")) → secStr
  22. If((x(P) / y(P) * 100) ≟ (round(x(P) / y(P), 2) * 100), " = ", " \approx ") → cotEquality
  23. If(y(P) ≟ 0, "\text{undefined}", (("\(" * x(P) / y(P)) * "\)")) → cotFinalFmt
  24. LaTeX(((((((("\text{\cot(\theta) = \dfrac{\(x\)}{\(y\)} = \dfrac{\(" * x(P)) * "\)}{\(") * y(P)) * "\)}") * cotEquality) * cotFinalFmt) * "}")) → cotStr
  25. TableText({{thetaStr, rStr, cscStr, secStr, cotStr}}, "vl") → displayData
  26. CurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, currAngle / 360) → angleCurve
  27. Polygon({(0, 0), (0, 0.5), (0.5, 0.5), (0.5, 0)}) → angleBoxTemplate
  28. Element(angleMeasures, currIndx) → test
  29. Translate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.5, x(P)], If[y(P) < 0, -0.5, 0])) → angleBox