单位圆 by Taylor
几何画板及绘图内容加载中,请稍等……
这个范例演示单位圆的几何构造。涉及的核心数学概念包括圆的性质、角度和三角函数。通过使用GeoGebra命令如Point、Segment、Polygon等,可以动态展示单位圆上的点、角度和三角函数值。适合初中及以上学生学习几何和三角函数。
GeoGebra 命令及参数
Point(c) → ASequence((π * k) / 12, k, 0, 24) → AnglesSequence((cos(Element[Angles306090, k]), sin(Element[Angles306090, k])), k, 1, 9) → Pts306090Segment(O, B) → dMin(abs(Angles306090 - acos(x(A)))) → d306090Min(abs(Angles459045 - acos(x(A)))) → d459045Min(abs(AnglesVH - acos(x(A)))) → dVHIf((d306090 ≤ d459045) ∧ (d306090 ≤ dVH), 1, 0) → is306090If((d459045 < d306090) ∧ (d459045 < dVH), 1, 0) → is459045If((dVH < d306090) ∧ (dVH < d459045), 1, 0) → isVHIf(y(A) > 0, acos(x(A)), π + acos(-x(A))) → thetaPolygon(O, A, B) → Triangle306090, b, o, aPolygon(O, A, B) → Triangle459045, b_1, o_1, a_1Polygon(O, A, B) → TriangleVH, b_2, o_2, a_2Sequence((cos(Element[Angles459045, k]), sin(Element[Angles459045, k])), k, 1, 4) → Pts459045Sequence((cos(Element[AnglesVH, k]), sin(Element[AnglesVH, k])), k, 1, 4) → PtsVHSequence((cos(Element[AnglesAll, k]), sin(Element[AnglesAll, k])), k, 1, Length[AnglesAll]) → PtsAllElement(AnglesAllLabels, 2) → FailRandom(1, 14) → randIntIf(theta > π, "-", "") → negSinIf((π / 2 < theta) ∧ (theta < (3 * π) / 2), "-", "") → negCosIf(tan(theta) < 0, "-", "") → negTanAngle(O2, O, A) → alphaGreenIf(theta ≟ π / 3 ∨ theta ≟ 2 * π / 3 ∨ theta ≟ 4 * π / 3 ∨ theta ≟ 5 * π / 3, 1) → isTall306090If(theta ≟ π / 6 ∨ theta ≟ 5 * π / 6 ∨ theta ≟ 7 * π / 6 ∨ theta ≟ 11 * π / 6, 1) → isSkinny306090If(theta ≟ π / 4 ∨ theta ≟ 3 * π / 4 ∨ theta ≟ 5 * π / 4 ∨ theta ≟ 7 * π / 4, 1) → isReal459045If(theta ≟ 0 ∨ theta ≟ π ∨ theta ≟ 2 * π, 1) → isHPoint(xAxis) → CPoint(xAxis) → DPoint(xAxis) → EPoint(xAxis) → FPoint(yAxis) → GPoint(yAxis) → HPoint(yAxis) → IPoint(yAxis) → JPoint(c_1) → A_1Point(c_2) → A_2Angle(O2, O, A) → alphaRedAngle(O2, O, A) → alphaBlue
AI 绘图提示语参考
绘制单位圆,从圆心O开始,画出30°、60°、90°等角度对应的点P,并连接这些点和圆心形成三角形。绘制45°、90°、45°等角度对应的点Q和三角形,以及所有角度对应的点R。在x轴上标记四个点C、D、E、F,在y轴上标记四个点G、H、I、J。
以上提示语为根据原始绘图命令整理而来,仅供参考。