单位圆的原理演示

几何画板及绘图内容加载中，请稍等……

2016-03-11 14:08

①本范例通过动态演示说明单位圆在三角函数中的几何意义；②涉及核心概念为单位圆、三角函数、直角三角形、特殊点；③作图要点运用了Function（函数）、Point（点）、Intersect（交点）、Line（直线）、Circle（圆）、Vector（向量）、Segment（线段）、OrthogonalLine（垂线）、Polygon（多边形）等GeoGebra命令；④适合高中数学教学，用于理解三角函数与单位圆的关系。

GeoGebra 命令及参数

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Point(p) → J
Point(p) → I
Intersect(xAxis, yAxis) → O
Line(O, B) → a
Circle(O, 1) → c
Intersect(c, a, 1) → C
Vector(B, C) → u
Line(O, A) → b
Intersect(c, b, 1) → D
Vector(A, D) → v
Segment(C, B) → d
Segment(D, A) → e
OrthogonalLine(E, xAxis) → f
OrthogonalLine(F, xAxis) → g
Intersect(f, xAxis) → G
Intersect(g, xAxis) → H
Polygon(O, E, G) → poly1, g_1, o, e_1
Polygon(O, F, H) → poly2, h, o_1, f_1
OrthogonalLine(A, xAxis) → k
OrthogonalLine(B, xAxis) → l
Intersect(l, xAxis) → L
Intersect(k, xAxis) → M
Polygon(O, M, A) → poly3, a_1, o_2, m
Polygon(O, B, L) → poly4, l_1, o_3, b_1

AI 绘图提示语参考

绘制单位圆，并在圆上标出关键点和向量。首先画出单位圆和坐标轴，然后在圆上找到与x轴垂直的点C和D，接着画出从原点到C和D的向量u和v，再画出与x轴垂直的直线f和g，确定它们与x轴的交点G和H，最后画出四个三角形，分别是OEG、OEH、OMA和OBL，以展示单位圆与向量的关系。

以上提示语为根据原始绘图命令整理而来，仅供参考。