30n°角的正弦与余弦几何构造与数值演示
几何画板及绘图内容加载中,请稍等……
本范例演示了 30 度整数倍角(30n°)的正弦与余弦值在单位圆上的几何分布规律。核心数学概念涵盖三角函数定义、角度序列及反射变换。作图要点包括使用 Circle 构建单位圆,利用 Mirror 和 Segment 绘制对应线段,通过 Polygon 和 Angle 展示角度关系,并结合 Point 与 Intersect 确定坐标点。该工具适合高中学生理解三角函数周期性,或教师用于课堂动态演示,帮助直观掌握特殊角的三角函数值。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → APoint(xAxis) → BCircle(A, B) → cIntersect(c, f, 1) → CIntersect(c, f, 2) → DIntersect(c, g, 2) → EIntersect(c, g, 1) → FMirror(E, xAxis) → E'Mirror(F, xAxis) → F'Mirror(C, yAxis) → C'Mirror(D, yAxis) → D'Intersect(c, xAxis, 2) → GIntersect(c, yAxis, 2) → HIntersect(c, yAxis, 1) → ISegment(A, E) → jSegment(A, E') → kSegment(E, E') → lPolygon(A, C', C) → poly2, n, p, qPolygon(A, E', E) → poly1, e, a, e'Segment(G, C') → mPolygon(A, F, F') → poly4, f', a_3, f_1Polygon(D, D', A) → poly5, r, s, tSegment(A, B) → bSegment(A, H) → dSegment(G, A) → g_1Segment(A, I) → h_1Intersect(i, l) → JSegment(A, J) → i_1Angle(E, J, A) → αIntersect(h, p) → KSegment(K, A) → j_1Angle(C', K, A) → βIntersect(i, a_3) → LSegment(L, A) → k_1Angle(F', L, A) → γIntersect(h, r) → MSegment(A, M) → l_1Angle(D, M, A) → δPolygon(P, N, O, Q) → poly3, p_1, n_1, o, q_1Polygon(P_1, N_1, O_1, Q_1) → poly3_1, p_2, n_2, o_1, q_2Polygon(P_2, N_2, O_2, Q_2) → poly3_2, p_3, n_3, o_2, q_3Polygon(P_3, N_3, O_3, Q_3) → poly3_3, p_4, n_4, o_3, q_4Polygon(P_4, N_4, O_4, Q_4) → poly3_4, p_5, n_5, o_4, q_5Polygon(P_5, N_5, O_5, Q_5) → poly3_5, p_6, n_6, o_5, q_6Polygon(P_6, N_6, O_6, Q_6) → poly3_6, p_7, n_7, o_6, q_7Polygon(P_7, N_7, O_7, Q_7) → poly3_7, p_8, n_8, o_7, q_8Polygon(P_8, N_8, O_8, Q_8) → poly3_8, p_9, n_9, o_8, q_9Polygon(P_9, N_9, O_9, Q_9) → poly3_9, p_{10}, n_{10}, o_9, q_{10}Polygon(P_{10}, N_{10}, O_{10}, Q_{10}) → poly3_{10}, p_{11}, n_{11}, o_{10}, q_{11}Polygon(P_{11}, N_{11}, O_{11}, Q_{11}) → poly3_{11}, p_{12}, n_{12}, o_{11}, q_{12}