互余三角比
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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
Sequence(i, i, 0, 357, 3) → angleMeasuresZip(((5 * cos(A°)), (5 * sin(A°))), A, angleMeasures) → pointListPoint(pointList) → PIndexOf(P, pointList) → currIndxIf(x(P) ≠ 0, 5 / x(P)) → D4UnicodeToLetter(10007) → xmarkUnicodeToLetter(10003) → cmarkSegment(P, (x(P), 0)) → VerticalLineVector((0, 0), (qWidth, 0)) → hAxisRotate(hAxis, π, (0, 0)) → hAxis2Rotate(hAxis, π / 2, (0, 0)) → vAxisRotate(hAxis, (3 * π / 2), (0, 0)) → vAxis2Element(angleMeasures, currIndx) → currAngleZip(Rotate[A, currAngle°, (0, 0)], A, {(1.8, -0.2), (2, 0), (2.2, -0.2)}) → chevronPointsSequence(Segment[Element[chevronPoints, i], Element[chevronPoints, i + 1]], i, 1, 2) → chevronIf((5 / y(P) * 100) ≟ (round(5 / y(P), 2) * 100), " = ", " \approx ") → cscEqualityIf(y(P) ≟ 0, "\text{undefined}", (("\(" * 5 / y(P)) * "\)")) → cscFinalFmtLaTeX(((((("\text{\csc(\theta) = \dfrac{\(r\)}{\(y\)} = \dfrac{\(5\)}{\(" * y(P)) * "\)}") * cscEquality) * cscFinalFmt) * "}")) → cscStrIf((5 / x(P) * 100) ≟ (round(5 / x(P), 2) * 100), " = ", " \approx ") → secEqualityIf(x(P) ≟ 0, "\text{undefined}", (("\(" * 5 / x(P)) * "\)")) → secFinalFmtLaTeX(((((("\text{\sec(\theta) = \dfrac{\(r\)}{\(x\)} = \dfrac{\(5\)}{\(" * x(P)) * "\)}") * secEquality) * secFinalFmt) * "}")) → secStrIf((x(P) / y(P) * 100) ≟ (round(x(P) / y(P), 2) * 100), " = ", " \approx ") → cotEqualityIf(y(P) ≟ 0, "\text{undefined}", (("\(" * x(P) / y(P)) * "\)")) → cotFinalFmtLaTeX(((((((("\text{\cot(\theta) = \dfrac{\(x\)}{\(y\)} = \dfrac{\(" * x(P)) * "\)}{\(") * y(P)) * "\)}") * cotEquality) * cotFinalFmt) * "}")) → cotStrTableText({{thetaStr, rStr, cscStr, secStr, cotStr}}, "vl") → displayDataCurveCartesian((2 * cos(((2 * π) * t))), (2 * sin(((2 * π) * t))), t, 0, currAngle / 360) → angleCurvePolygon({(0, 0), (0, 0.5), (0.5, 0.5), (0.5, 0)}) → angleBoxTemplateElement(angleMeasures, currIndx) → testTranslate(angleBoxTemplate, (If[x(P) > 0, x(P) - 0.5, x(P)], If[y(P) < 0, -0.5, 0])) → angleBox