单位圆与反三角函数图像
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①本范例演示单位圆与正弦、余弦、正切及反三角函数图像的关系;②涉及核心数学概念包括单位圆定义、三角函数、反三角函数、导数、解析几何;③作图要点运用了Line(线)、Point(点)、Segment(线段)、Intersect(交点)、Circle(圆)、Angle(角)、OrthogonalLine(垂线)等GeoGebra命令;④适合高中及以上数学学习,用于理解三角函数性质及图像变换。
GeoGebra 命令及参数
Line(A, xAxis) → aPoint(a) → B_1Segment(A, B_1) → bIntersect(xAxis, yAxis) → DCircle(A, b) → cPoint(c) → CSegment(A, C) → dAngle(B_1, A, C) → αPoint(Circle[D, α]) → ESegment(D, E) → eOrthogonalLine(C, b) → h_1Intersect(h_1, a) → FSegment(C, F) → SineIntersect(c, a, 2) → GSegment(G, A) → iSegment(A, F) → CosineOrthogonalLine(C, d) → jIntersect(a, j) → HSegment(C, H) → TangentSegment(B_1, H) → k_1OrthogonalLine(E, xAxis) → lIntersect(g, l, (0.6775728175269462, 0.782731011348612)) → IIntersect(f, l, (0.6775728175269462, 0.6298282915862481)) → JIntersect(n, l, (0.6775728175269462, 0.8084084484644634)) → KSegment(J, E) → qSegment(I, E) → rSegment(K, E) → pIntersect(f_1, l, (0.6775728175269462, 1.6025820473500487)) → LIntersect(g_1, l, (0.6775728175269462, 1.289525390427809)) → MIntersect(n_1, l, (0.6775728175269462, 1.2485662599475453)) → NOrthogonalLine(C, d) → a_1OrthogonalLine(A, i) → b_1Intersect(a_1, b_1) → OSegment(O, C) → CotangentOrthogonalLine(N, xAxis) → c_1Intersect(c_1, xAxis) → PSegment(N, P) → d_1Line(A, B_1) → sOrthogonalLine(C, d) → e_1Intersect(s, e_1) → QSegment(C, Q) → i_1Segment(A, Q) → SecantOrthogonalLine(M, xAxis) → j_1Intersect(j_1, xAxis) → RSegment(M, R) → l_1OrthogonalLine(A, i) → m_1OrthogonalLine(C, d) → p_1Intersect(m_1, p_1) → SSegment(S, A) → CosecantOrthogonalLine(L, xAxis) → q_1Intersect(q_1, xAxis) → TSegment(L, T) → r_1Intersect(c, b, 1) → U
AI 绘图提示语参考
绘制单位圆及其与正弦、余弦、正切和反正弦函数的关系图。首先画出x轴和单位圆,然后通过单位圆上的点绘制正弦、余弦和正切线段,接着画出反三角函数的图像,最后连接关键点形成单位圆和反三角函数的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。